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Cute Divisibility (Posted on 2013-01-26)

Given that a number L = (3³⁹+5³⁹)/4 + 1,

is (3^L+5^L)/4 +1 divisible by L ?

If so, prove it.

No Solution Yet Submitted by Danish Ahmed Khan

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other thoughts

Comment 2 of 2 |

If f(L) = (3^L + 5^L)/4 + 1,

then f(1) = 3 and f(f(1)) = 39.

Also the sum of 39th powers is divisible by (3^3 + 5^3) = 152, so the given value of L is of the form 38k + 1.

Posted by xdog on 2013-01-27 11:34:31

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