A positive integer
at least of size 3 is called polite if it can be written in at least one way as the sum of two or more consecutive positive integers
The Beal Conjecture states that the only solutions to the equation Ax + By = Cz, when A, B, C, are positive integers
, and x, y, and z are positive integers
greater than two, are those in which A, B, and C have a common factor.
r]) is an r-tuple of positive integers
and j = ([j.
Among these messages there are some which characterize or define positive integers
, sometimes in any of several ways.
A pair of positive integers
(m, n) (with n > m) is called the Smarandache friendly numbers if
He identifies stages in solving equations during the intervening millennia, linking them to successive extensions of the number systems beyond positive integers
and fractions to embrace positive irrational numbers, negative numbers timidly towards the end of the Middle Ages, and finally complex numbers shortly after that.
If N [greater than or equal to] 1 the Euler totient function [phi](N) is the number of positive integers
not exceeding N, which are relatively prime to N.
m]), where, m n [member of] n, the set of positive integers
Given Lagrange's result, number theorists asked whether there are other such expressions, called quadratic forms, that also repre sent all positive integers
It is noted that if p + [pi]/k = q + [pi]/m for rational numbers p and q and positive integers
k and m, then p = q and k = m.
Prove that for every i = 0, 1, 2, 3, there are infinitely many positive integers
n such that there are exactly i good numbers among n, n + 2, and n + 28.
Given any two consecutive positive integers
, the difference in their squares is equal to their sum.