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Math for the people, by the people.

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PlanetMath is a virtual community which aims to help make mathematical knowledge more accessible. PlanetMath's content is created collaboratively: the main feature is the mathematics encyclopedia with entries written and reviewed by members. The entries are contributed under the terms of the Creative Commons By/Share-Alike License in order to preserve the rights of authors, readers and other content creators in a sensible way. We use LaTeX, the lingua franca of the worldwide mathematical community.

Beginning February 23th 2015 we experienced 15 days of downtime when our server stopped working. We moved a backup to DigitalOcean, and we're back online. Some features aren't working yet; we're restoring them ASAP. Please report bugs in the Planetary Bugs Forum or on Github.

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Latest Messages  

[P] How to find valid bases for pseudoprimes in Z(i) by akdevaraj Aug 24
We can use pari. There is another way: Take a known base for pseudoprimality of a composite number. Split it into two parts such that one part is exactly divisible by one or more prime factors of the given composite number and the other is exactly divisible by the remaining prime factor/s. Let any one of the two parts be the real and the other be the coefficient of i in the complex base. Example: 29 is a base for pseudo -primality of 105 in Z. 29 can be split into two parts 14 and 15. 14 is divisible by 7 and 15 is divisible by 3 and 5. Hence 14 + 15i and 15 + 14i are valid bases in Z(i). Needless to say conjugates of these two are also valid bases.

[P] Using pari to find valid bases for pseudoprimes(contd) by akdevaraj Aug 23
I was looking for something predictable in finding valid bases for pseudoprimality of 105. Happy to say that I succeeded: starting from 41, 41 + 21*k, where k belongs to N are valid bases; exceptions - integers ending with 0 or 5. Needless to say there are bases other than these.

[P] Using pari to find valid bases for pseudoprimes(contd) by akdevaraj Aug 21
In Z(i) (20 + 21*i) and (21 + 20*i) are valid bases for pseudoprimality of 105. Needless to say their conjugates are also valid bases.

[P] Using pari to find valid bases for pseudoprimes(contd) by akdevaraj Aug 21
Not only 29, but also 41, 43, 62, 64, 71, 76, 83, 92, 97 and 104 are valid bases for pseudoprimality of 105.

[P] Search facility by akdevaraj Aug 18
Perhaps bc1 can help administration to restore the search facility.

[P] Search facility by akdevaraj Aug 18
Perhaps bc1 can help administration to restore the search facility.

[P] Search facility by akdevaraj Aug 18
Perhaps bc1 can help administration to restore the search facility.

[P] Using pari to find valid bases for pseudoprimes by akdevaraj Aug 18
Supposing we wish to find the base for which 77 is a pseudoprime we can use pari. The programme: {p(n) =(n^76-1)/77} for(n=1, 60,print (p(n))). Thus I found that 34 is a valid base for pseudoprimality of 77.

[P] Wanted: volunteer to make following entry by akdevaraj Aug 18
Would be glad if some member would volunteer to make the following entry in maths encyclopedia: Mangammal primes: These are the impossible prime factors of (3^n - 2). see A 123239 in OEIS. This is a corollary of Ëuler's generalisation of Fermat's theore- a further generalisation (ISSN 1550-3747 ).

[P] Wanted: volunteer to make following entry by akdevaraj Aug 17
Would be glad if some member would volunteer to make the following entry in maths encyclopedia: Mangammal primes: These are the impossible prime factors of (3^n - 2). see A 123239 in OEIS. This is a corollary of Ëuler's generalisation of Fermat's theore- a further generalisation (ISSN 1550-3747 ).

[P] Wanted: volunteer to make following entry by akdevaraj Aug 17
Would be glad if some member would volunteer to make the following entry in maths encyclopedia: Mangammal primes: These are the impossible prime factors of (3^n - 2). see A 123239 in OEIS. This is a corollary of Ëuler's generalisation of Fermat's theore- a further generalisation (ISSN 1550-3747 ).

[P] Wanted: volunteer to make following entry by akdevaraj Aug 17
Would be glad if some member would volunteer to make the following entry in maths encyclopedia: Mangammal primes: These are the impossible prime factors of (3^n - 2). see A 123239 in OEIS. This is a corollary of Ëuler's generalisation of Fermat's theore- a further generalisation (ISSN 1550-3747 ).

[P] Wanted: volunteer to make following entry by akdevaraj Aug 17
Would be glad if some member would volunteer to make the following entry in maths encyclopedia: Mangammal primes: These are the impossible prime factors of (3^n - 2). see A 123239 in OEIS. This is a corollary of Ëuler's generalisation of Fermat's theore- a further generalisation (ISSN 1550-3747 ).

[P] Wanted: volunteer to make following entry by akdevaraj Aug 17
Would be glad if some member would volunteer to make the following entry in maths encyclopedia: Mangammal primes: These are the impossible prime factors of (3^n - 2). see A 123239 in OEIS. This is a corollary of Ëuler's generalisation of Fermat's theore- a further generalisation (ISSN 1550-3747 ).