MathDB

10

Part of 2017 Moldova Team Selection Test

Problems(1)

MDA TST B10, floor function problem

Source: Moldova 2017 TSTST, B10

3/20/2017
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.
number theory