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

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

If so, prove it.

I don't know if this helps, but L factors as follows:

L = 454747351899602907212263599 = 3 * 13 * 71 * 876751 * 187314308380106321

so L is itself divisible by 39.

Posted by Charlie on 2013-01-27 10:27:49