Here's a proof: http://mathforum.org/library/drmath/view/67256.html …
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Probably the first tweet here I understood fully
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That's why 42 is the answer to life!
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Prove: the difference of two-digit reversed squares is always divisible by 99. E.g. 41^2 - 14^2 = 15 x 99.
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I think this has something to do with the base number system your using so with base 10 this will be divisible by 99. In base 8 for example the difference of the squares of the reversed double digits would be divisible by 77 (ie 63 as described in base 10)
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Giving positive example does not prove possibility but giving negative example prove impossibility. This is a good example for this rule.
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2 is the weirdest of all numbers
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... and (trivially) the only positive integer solution to b^a = a^(a^a)
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Does anybody know where to find the proof?
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Take the log, assume you can divide. You have to solve ln(x)/x=ln(y)/y. Study the function x->ln(x)/x it has a max at x=e. So since x>1 you only have to study x=2 and find the other solution.
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