parity of function
Thus the total number of the divisors is
From this we see that in to be an odd number, every sum shall be odd, i.e. every exponent in (1) must be even. It means that has an even number of each of its prime divisors ; so is a square of an integer, a perfect square.
Consequently, the number of all positive divisors of an integer is always even, except if the integer is a perfect square.
Examples. 15 has four positive divisors 1, 3, 5, 15 and the square number 16 five divisors
1, 2, 4, 8, 16.
|Title||parity of function|
|Date of creation||2013-03-22 18:55:43|
|Last modified on||2013-03-22 18:55:43|
|Last modified by||pahio (2872)|