User huan xiong - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T06:59:10Z http://mathoverflow.net/feeds/user/11721 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/49961/the-number-of-different-prime-factors-of-a-special-class-of-positive-integers The number of different prime factors of a special class of positive integers Huan Xiong 2010-12-20T13:28:49Z 2011-02-01T13:02:59Z <p>Let $m_i\geq 2 (1\leq i\leq n)$ be $n$ pairwisely coprime positive integers and let $q_i\geq 2 (1\leq i\leq n)$ be $n$ arbitrary prime powers, let$A=\prod_{i=1}^n(({q_i}^{m_i}-1)/(q_i-1))$. Let $\sigma(A)$ be the number of different prime factors of A, is it true that $\sigma(A)\geq n$? If this is not true, is there a counterexample? Is there a good way to estimate $\sigma(A)$?</p>