Difference between revisions of "2006 SMT/Algebra Problems/Problem 7"
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Latest revision as of 09:40, 28 May 2012
Problem
Find all solutions to , where and are nonzero digits, and is an integer. ( and are not necessarily distinct.)
Solution
Notice that . Therefore, must be divisible by . Since is prime, either or must be a multiple of . However, if , then , so we only need to consider when . In this case, , a solution, so the only solution is .