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MDA TST B10, floor function problem

Source: Moldova 2017 TSTST, B10

March 20, 2017
number theory

Problem Statement

Let pp be an odd prime. Prove that the number ⌊(5+2)p−2p+1⌋\left\lfloor \left(\sqrt{5}+2\right)^{p}-2^{p+1}\right\rfloor is divisible by 20p20p.
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