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 April 20th, 2010, 10:18 AM #1 Newbie   Joined: Apr 2010 Posts: 4 Thanks: 0 Some math expert? look at this Consider the equation a ? x ? 4 Z_64 (the integers modulo 64), where a is an integer 0 ? a ? 63 For what values of the equation has a one or more solutions? (Ie for what values of a there are one or more x, so that a ? x ? 4 mod. 64?
 April 21st, 2010, 03:33 PM #2 Member   Joined: Mar 2010 Posts: 32 Thanks: 0 Re: Some math expert? look at this If $8|a$ then there's no chance because then $ax-4=4(2k-1)$ for some $k$. Otherwise $a=\hat{a}2^r$ with $r\leq 2$ and $(\hat{a},2)=1$. Then $2^{2-r}b$ will be a solution, where $\hat{a}b\equiv 1(64)$. So the answer is when $a$ is not a multiple of 8.

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