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About
References to 'divisibility'
1.
$n$-free number
by
Wkbj79
2.
$n$-full number
by
Wkbj79
3.
$n$-section of line segment with compass and straightedge
by
pahio
4.
$p$-adic integers
by
djao
5.
$x^4-y^4=z^2$ has no solutions in positive integers
by
rm50
6.
$y^2= x^3-2$
by
CWoo
7.
$\mathrm{lcm}(ma,mb) =m \mathrm{lcm}(a,b)$
by
drini
8.
${\mathbb{Z}}_n$
by
Wkbj79
9.
a demonstration of different encryption methods on the same sample message
by
PrimeFan
10.
a few examples of solutions to Zn\'am's problem
by
PrimeFan
11.
a group of even order contains an element of order 2
by
azdbacks4234
12.
a lecture on the partial fraction decomposition method
by
alozano
13.
a polynomial of degree $n$ over a field has at most $n$ roots
by
alozano
14.
a prime occurs in the Euclid-Mullin sequence no more than once
by
PrimeFan
15.
abundant number
by
CompositeFan
16.
affine combination
by
CWoo
17.
algebraic number theory
by
alozano
18.
algorithm
by
jk81
19.
algorithm for modular exponentiation
by
PrimeFan
20.
all positive integers are polite numbers except powers of two
by
PrimeFan
21.
All unnatural square roots are irrational
by
ubershmekel
22.
amenable number
by
PrimeFan
23.
analytic continuation of Riemann zeta (using integral)
by
rspuzio
24.
any nonzero integer is quadratic residue
by
pahio
25.
Basel problem derivation
by
curious
26.
Beal conjecture
by
mathcam
27.
Bertrand's conjecture, proof of
by
CWoo
28.
binomial theorem, proof of
by
mps
29.
biquadratic field
by
Wkbj79
30.
Black-Scholes formula
by
stevecheng
31.
bounds on $\pi(n)$
by
rm50
32.
Brun's pure sieve
by
bbukh
33.
calculating the Jacobi symbol
by
mathwizard
34.
calculating the splitting of primes
by
mathcam
35.
Cantor-Zassenhaus split
by
mathwizard
36.
Cardano's derivation of the cubic formula
by
djao
37.
Carmichael function
by
PrimeFan
38.
center of gravity of circular sector
by
curious
39.
central binomial coefficient
by
rspuzio
40.
centroid
by
drini
41.
characterization of abelian extensions of exponent n
by
rm50
42.
characterization of prime ideals
by
GrafZahl
43.
Chen prime
by
PrimeFan
44.
Chinese hypothesis
by
FourDozens
45.
Chinese remainder theorem in terms of divisor theory
by
pahio
46.
Chinese remainder theorem proof
by
vampyr
47.
class number divisibility in cyclic extensions
by
alozano
48.
class number divisibility in extensions
by
alozano
49.
classical groups
by
Algeboy
50.
colossally abundant number
by
CompositeFan
51.
common point of triangle medians
by
pahio
52.
computer representation of integers
by
rm50
53.
congruence
by
rspuzio
54.
congruence in algebraic number field
by
pahio
55.
congruence of Clausen and von Staudt
by
alozano
56.
constructible angles with integer values in degrees
by
PrimeFan
57.
convergents to a continued fraction
by
rm50
58.
converse of Wilson's theorem
by
PrimeFan
59.
covering system
by
PrimeFan
60.
criteria for cyclic rings to be isomorphic
by
Wkbj79
61.
criterion of N\'eron-Ogg-Shafarevich
by
alozano
62.
cryptography
by
CWoo
63.
cryptography and number theory
by
archibal
64.
cubic reciprocity law
by
mathcam
65.
Cullen number
by
PrimeFan
66.
cyclic number
by
PrimeFan
67.
cyclic rings and zero rings
by
Wkbj79
68.
de Polignac's formula
by
PrimeFan
69.
decimal expansion
by
pahio
70.
derivation of 2D reflection matrix
by
stevecheng
71.
derivation of half-angle formulae for tangent
by
rspuzio
72.
derivation of mutual information
by
tdunning
73.
derivation of quadratic formula
by
mathcam
74.
derivation of unit vectors in curvilinear coordinates
by
swapnizzle
75.
derivatives by pure algebra
by
Algeboy
76.
Descartes' rule of signs
by
PrimeFan
77.
determination of abundant numbers with specified prime factors
by
rspuzio
78.
determination of even abundant numbers with one odd prime factor
by
rspuzio
79.
determining the continuations of exponent
by
pahio
80.
developable surface
by
pahio
81.
differential equations for $x^x$
by
rspuzio
82.
differential form
by
rmilson
83.
digitaddition generator
by
PrimeFan
84.
direct integral of Hilbert spaces
by
rspuzio
85.
discriminant of algebraic number
by
pahio
86.
divisibility by prime number
by
pahio
87.
divisibility by product
by
pahio
88.
divisibility of central binomial coefficient
by
rspuzio
89.
divisibility of nine-numbers
by
pahio
90.
divisibility test
by
CompositeFan
91.
divisor as factor of principal divisor
by
pahio
92.
double Mersenne number
by
PrimeFan
93.
doubling and halving algorithm for integer multiplication
by
CompositeFan
94.
duodecimal
by
PrimeFan
95.
e is transcendental
by
pahio
96.
Egyptian geometry areas calculated in, cubits, khets and setats
by
milogardner
97.
Egyptian weights and measures, hekat divisions
by
milogardner
98.
Eisenstein criterion
by
Daume
99.
elementary proof of orders
by
Algeboy
100.
elementary results about multiplicative functions and convolution
by
Wkbj79
101.
elliptic curve
by
djao
102.
elliptic curve cryptography
by
PrimeFan
103.
equivalence relation
by
CWoo
104.
equivalent definitions for UFD
by
joking
105.
Erd\H{o}s-Woods number
by
PrimeFan
106.
Euclid's lemma proof
by
akrowne
107.
Euler product
by
bbukh
108.
every even integer greater than 70 is the sum of two abundant numbers in more than one way
by
PrimeFan
109.
every PID is a UFD
by
rm50
110.
every positive integer greater than 30 has at least one composite totative
by
mps
111.
every prime has a primitive root
by
alozano
112.
every sufficiently large even integer can be expressed as the sum of a pair of abundant numbers
by
rspuzio
113.
exact sequence
by
djao
114.
exactly divides
by
Wkbj79
115.
example of gcd
by
pahio
116.
example of group action
by
Thomas Heye
117.
example of non-diagonalizable matrices
by
cvalente
118.
example of normal extension
by
alozano
119.
examples of 1-automorphic numbers
by
PrimeFan
120.
examples of Cauchy-Riemann equations
by
rspuzio
121.
examples of cyclotomic polynomials
by
alozano
122.
examples of digital roots in a few selected bases
by
PrimeFan
123.
examples of minimal polynomials
by
Wkbj79
124.
examples of non-matrix Lie groups
by
bwebste
125.
examples of perfect totient numbers
by
PrimeFan
126.
examples of Pollard's $p - 1$ algorithm on a few integers
by
PrimeFan
127.
examples of prime ideal decomposition in number fields
by
alozano
128.
examples of radicals of ideals in commutative rings
by
joking
129.
examples of ranges of consecutive integers for Erd\H{o}s-Woods numbers
by
PrimeFan
130.
examples of regular primes
by
alozano
131.
examples of semigroups
by
CWoo
132.
examples of the Lucas-Lehmer primality test on small numbers
by
PrimeFan
133.
existence and uniqueness of the gcd of two integers
by
alozano
134.
existence of maximal semilattice decomposition
by
mclase
135.
expressing fractions in factorial base
by
rspuzio
136.
extensions without unramified subextensions and class number divisibility
by
alozano
137.
factor theorem
by
drini
138.
factorial prime
by
PrimeFan
139.
factoring all-one polynomials using the grouping method
by
rspuzio
140.
Factorization of the Dedekind zeta function of an abelian number field
by
alozano
141.
factors of $n$ and $x^n-1$
by
pahio
142.
Fermat numbers
by
drini
143.
Fermat numbers are coprime
by
yark
144.
field is discrete and cocompact in its ad\`{e}les
by
rm50
145.
formal congruence
by
pahio
146.
formula for sum of divisors
by
rspuzio
147.
Fourier transform
by
mathwizard
148.
fraction
by
bwebste
149.
fraction power
by
pahio
150.
free commutative algebra
by
Algeboy
151.
freshman's dream
by
Algeboy
152.
fundamental theorem of arithmetic
by
CWoo
153.
fundamental theorem of arithmetic, proof of the
by
mps
154.
Galois groups of finite abelian extensions of $\mathbb{Q}$
by
Wkbj79
155.
Galois representation
by
alozano
156.
Gauss' lemma
by
drini
157.
generalized binomial coefficients
by
pahio
158.
generalized B\'ezout theorem on matrices
by
perucho
159.
generalized Pythagorean theorem
by
yogis
160.
geometric proof of Pythagorean triplet
by
rm50
161.
Giuga number
by
Mravinci
162.
Goniometric solution of cubic equation
by
Altair
163.
googol
by
Mathprof
164.
greatest common divisor
by
CWoo
165.
group cohomology (topological definition)
by
whm22
166.
grouplike elements in Hopf algebras
by
joking
167.
G\"{o}del's beta function
by
gribskoff
168.
harmonic oscillator
by
perucho
169.
Harshad number
by
PrimeFan
170.
henselian field
by
mps
171.
Hermite's theorem
by
alozano
172.
Hermitian dot product (finite fields)
by
GrafZahl
173.
hexadecimal
by
PrimeFan
174.
highly composite number
by
Kevin OBryant
175.
how to multiply polynomials
by
Algeboy
176.
hyperperfect number
by
CompositeFan
177.
ideal class group is finite
by
rm50
178.
if $\mu(n) = (-1)^{\omega(n)}$ then $\tau(n) = 2^{\omega(n)}$
by
1and2and4
179.
implications of having divisor theory
by
pahio
180.
incidence structure
by
CWoo
181.
index of tables
by
PrimeFan
182.
index of the group of cyclotomic units in the full unit group
by
alozano
183.
indirect proof of identity theorem of power series
by
pahio
184.
inductive proof of Fermat's little theorem proof
by
mathcam
185.
inductively ordered
by
rspuzio
186.
inertial degree
by
djao
187.
integer contraharmonic means
by
pahio
188.
integral binary quadratic forms
by
rm50
189.
introducing 0th power
by
mathcam
190.
irreducible polynomial
by
pahio
191.
isotropy representation
by
rmilson
192.
iterated sum of divisors function
by
PrimeFan
193.
Ivan Pervushin
by
Mravinci
194.
Kummer's congruence
by
alozano
195.
Laplace equation in cylindrical coordinates
by
bloftin
196.
lecture notes on determinants
by
rmilson
197.
lecture notes on the Cayley-Hamilton theorem
by
rmilson
198.
lengths of angle bisectors
by
pahio
199.
list of divisors of some small highly composite numbers
by
PrimeFan
200.
long division
by
alozano
201.
Lucas-Carmichael number
by
PrimeFan
202.
Lucas-Lehmer primality test
by
CWoo
203.
mathematics vocabulary
by
matte
204.
maximal element
by
akrowne
205.
Mersenne numbers
by
alozano
206.
Mersenne numbers, two small results on
by
Cosmin
207.
method for representing rational numbers as sums of unit fractions using practical numbers
by
PrimeFan
208.
methods to find extremum
by
bloftin
209.
Miller-Rabin prime test
by
mathwizard
210.
minimal polynomial
by
Wkbj79
211.
modular group
by
rm50
212.
modular theory
by
Algeboy
213.
motivation for Euclidean domains
by
Wkbj79
214.
multiplication
by
PrimeFan
215.
multiplication operator
by
PrimeFan
216.
M\"obius function
by
mps
217.
M\"obius inversion
by
mathcam
218.
natural boundary
by
rspuzio
219.
needle-in-the-haystack
by
Algeboy
220.
non-constant element of rational function field
by
pahio
221.
normal extension
by
djao
222.
normality of subgroups of prime index
by
azdbacks4234
223.
nowhere differentiable
by
gel
224.
opus number
by
PrimeFan
225.
order valuation
by
pahio
226.
organismic supercategories and super-complex systems biodynamics
by
bci1
227.
p-adic exponential and p-adic logarithm
by
alozano
228.
palindromic prime
by
PrimeFan
229.
parity of $\tau$ function
by
pahio
230.
partial fractions
by
pahio
231.
partial fractions for polynomials
by
stevecheng
232.
partial fractions in Euclidean domains
by
stevecheng
233.
parts of a ball
by
pahio
234.
Pell's equation
by
rm50
235.
perfect number
by
Wkbj79
236.
perfect totient number
by
CompositeFan
237.
periodicity of a Markov chain
by
CWoo
238.
Pollard's $p - 1$ algorithm
by
PrimeFan
239.
Pollard's $\rho$
by
yark
240.
Pollard's $\rho$ algorithm
by
PrimeFan
241.
polyhedron
by
Mathprof
242.
positive multiple of a semiperfect number is also semiperfect
by
PrimeFan
243.
positive multiple of an abundant number is abundant
by
Mathprof
244.
potential of hollow ball
by
pahio
245.
power of an integer
by
rspuzio
246.
practical number
by
CompositeFan
247.
practical number
by
mathcam
248.
Pratt certificate
by
PrimeFan
249.
predicativism
by
gribskoff
250.
primality
by
PrimeFan
251.
primality testing
by
PrimeFan
252.
primary ideal
by
mathcam
253.
prime factors of $x^n-1$
by
pahio
254.
prime ideal decomposition in quadratic extensions of $\mathbb{Q}$
by
alozano
255.
prime ideal factorization is unique
by
gel
256.
prime quadruplet
by
PrimeFan
257.
primitive element of biquadratic field
by
Wkbj79
258.
projective line configurations
by
rspuzio
259.
proof of a corollary to Euler-Fermat theorem
by
alozano
260.
proof of all positive integers are polite numbers except powers of two
by
n847530
261.
proof of basis of ideal in algebraic number field
by
lalberti
262.
proof of Cauchy-Davenport theorem
by
Wolfgang
263.
proof of Cayley-Hamilton theorem in a commutative ring
by
Mathprof
264.
proof of Chinese remainder theorem
by
mclase
265.
proof of cyclic vector theorem
by
CWoo
266.
proof of determinant of the Vandermonde matrix
by
rspuzio
267.
proof of division algorithm for integers
by
drini
268.
proof of equivalence of definitions of valuation
by
rspuzio
269.
proof of Euler-Fermat theorem
by
KimJ
270.
proof of Euler-Fermat theorem using Lagrange's theorem
by
alozano
271.
proof of factor theorem using division
by
alozano
272.
proof of Fermat's little theorem using Lagrange's theorem
by
alozano
273.
proof of fundamental theorem of Galois theory
by
pbruin
274.
proof of general Stokes theorem
by
paolini
275.
proof of Goursat's theorem
by
rmilson
276.
proof of identity theorem of power series
by
rspuzio
277.
proof of inequalities for difference of powers
by
Mathprof
278.
proof of Lagrange's four-square theorem
by
CWoo
279.
proof of Lindemann-Weierstrass theorem and that e and $\pi$ are transcendental
by
rm50
280.
proof of Lucas-Lehmer primality test
by
rm50
281.
proof of Minkowski inequality
by
Andrea Ambrosio
282.
proof of necessary and sufficient condition for diagonalizability
by
rspuzio
283.
proof of norm and trace of algebraic number
by
Wkbj79
284.
proof of Ostrowski's valuation theorem
by
rm50
285.
proof of prime ideal decomposition in quadratic extensions of $\mathbb{Q}$
by
Wkbj79
286.
proof of Pythagorean triples
by
fredlb
287.
Proof of Stolz-Cesaro theorem
by
slash
288.
proof of Thue's Lemma
by
mathcam
289.
proof of Wilson's theorem
by
Cosmin
290.
proof of Wilson's theorem using the Wilson quotient
by
PrimeFan
291.
proof that $4^x$ exceeds the product of the primes up to $x$
by
PrimeFan
292.
proof that $\sqrt{2}$ is irrational
by
Wkbj79
293.
proof that $\tau(n)$ is the number of positive divisors of $n$
by
Wkbj79
294.
proof that a domain is Dedekind if its ideals are products of primes
by
gel
295.
proof that Sylvester's matrix equals the resultant
by
rspuzio
296.
proof that there are infinitely many primes using the Mersenne primes
by
PrimeFan
297.
properties of a gcd domain
by
CWoo
298.
properties of primitive roots
by
alozano
299.
properties of the multiplicative order of an integer
by
alozano
300.
proposed elementary proof of Fermat's last theorem
by
Mathprof
301.
Prosthaphaeresis formulas
by
mathfanatic
302.
pseudoprime
by
CompositeFan
303.
pure cubic field
by
Wkbj79
304.
Pythagorean triplet
by
drini
305.
quadratic extension
by
CWoo
306.
quadratic map
by
Algeboy
307.
quadratic sieve
by
patrickwonders
308.
quartic polynomial with Galois group $D_8$
by
rm50
309.
ramification index
by
djao
310.
rational sine and cosine
by
pahio
311.
recursive set
by
CWoo
312.
reduced word
by
Mazzu
313.
reduction formulas
by
curious
314.
reduction of elliptic integrals to standard form
by
rspuzio
315.
regular prime
by
djao
316.
Reisner Papyrus
by
milogardner
317.
remainder arithmetic
by
milogardner
318.
repdigit
by
CompositeFan
319.
representing primes as $x^2+ny^2$
by
rm50
320.
resultant
by
Mathprof
321.
Riemann zeta function has no zeros on $\Re s=0,1$
by
rm50
322.
Riemann-Hurwitz theorem
by
alozano
323.
rings of rational numbers
by
pahio
324.
root
by
mathcam
325.
rough number
by
PrimeFan
326.
rules of calculus for derivative of polynomial
by
rspuzio
327.
safe prime
by
PrimeFan
328.
scalar factor transfer rules
by
pahio
329.
Schinzel's Hypothesis H
by
jtolliver
330.
second proof of Wedderburn's theorem
by
Mathprof
331.
semiperfect number
by
CompositeFan
332.
separable
by
djao
333.
Sharkovskii's theorem
by
Koro
334.
sieve of Eratosthenes
by
mathcam
335.
Simon Stevin
by
PrimeFan
336.
Simple analytic discussion of the cubic equation
by
Altair
337.
simplicial category
by
mhale
338.
Smarandache function
by
dankomed
339.
Smith number
by
CompositeFan
340.
smooth number
by
CompositeFan
341.
solution of $1/x + 1/y = 1/n$
by
rspuzio
342.
sphenic number
by
CompositeFan
343.
splitting and ramification in number fields and Galois extensions
by
alozano
344.
splitting field
by
djao
345.
square-free number
by
akrowne
346.
squarefree factorization
by
mathwizard
347.
Stickelberger's theorem
by
mathcam
348.
Stirling's approximation
by
drini
349.
strong prime
by
PrimeFan
350.
structure of $(\mathbb{Z}/n\mathbb{Z})^{\times}$ as an abelian group
by
rm50
351.
subgroups of finite cyclic group
by
pahio
352.
sum of ideals
by
pahio
353.
sum of powers
by
CWoo
354.
summation
by
drini
355.
supercomputers
by
bci1
356.
superperfect number
by
CompositeFan
357.
Sylow theorems
by
yark
358.
table of factors of small Mersenne numbers
by
PrimeFan
359.
table of pseudoprimes below 2000 in bases 2 to 16
by
PrimeFan
360.
the difference of two odd squares is always a multiple of 8
by
PrimeFan
361.
the prime power dividing a factorial
by
Thomas Heye
362.
the torsion subgroup of an elliptic curve injects in the reduction of the curve
by
alozano
363.
theory from orders of classical groups
by
Algeboy
364.
there are an infinite number of primes $\equiv 1\mod m$
by
rm50
365.
there are an infinite number of primes $\equiv \pm 1\pmod 4$
by
rm50
366.
top ten coolest numbers
by
rspuzio
367.
topics on ideal class groups and discriminants
by
alozano
368.
trace forms on algebras
by
Algeboy
369.
trial division
by
CompositeFan
370.
UFD
by
drini
371.
ultrametric triangle inequality
by
pahio
372.
uncertainty theorem
by
dh2718
373.
unique factorization and ideals in ring of integers
by
pahio
374.
unitary divisor
by
CompositeFan
375.
unitary perfect number
by
CompositeFan
376.
unramified extensions and class number divisibility
by
alozano
377.
upper bound on $\vartheta(n)$
by
mps
378.
values of $n$ for which $\varphi(n)=\tau(n)$
by
Wkbj79
379.
Vandiver's conjecture
by
mathcam
380.
vector identities
by
mark_t314159
381.
volume of solid of revolution
by
pahio
382.
Wall-Sun-Sun prime
by
PrimeFan
383.
weird number
by
CompositeFan
384.
wheel factorization
by
PrimeFan
385.
Wieferich prime
by
mathcam
386.
Wilson prime
by
PrimeFan
387.
Wilson's theorem for prime powers
by
Thomas Heye
388.
zeroes of analytic functions are isolated
by
brianbirgen
389.
Zolotarev's lemma
by
mathcam
390.
Zsigmondy's theorem
by
lieven
391.
Zuckerman number
by
CompositeFan
392.
\'etale fundamental group
by
archibal
393.
\v{S}tefan Zn\'am
by
Mravinci