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Cute Divisibility (
Posted on 20130126
)
Given that a number L = (3
^{39}
+5
^{39}
)/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 20130127 11:34:31
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