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March 6th, 2012, 07:21 PM   #1
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A problem for the year 2012

Well, I have been looking through some old problems from famous math contests and a lot of them seem to have problems that have the number of the current year in them, so in the spirit of these math contests I came up with such a problem. I actually was unable to solve the last challenge that I posted. I kept approaching it in different ways and thinking that I had a proof, but there was always something wrong with it. However, in my efforts to solve that problem I discovered a few patterns, and this problem is the result of my hard work:

Prove that the equation

has no solutions in positive integers such that none of the are divisible by 503.
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