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Cute Divisibility (Posted on 2013-01-26) Difficulty: 3 of 5
Given that a number L = (339+539)/4 + 1,

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

If so, prove it.

No Solution Yet Submitted by Danish Ahmed Khan    
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Some Thoughts thoughts | Comment 1 of 2

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
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