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Divisible by 6 & 7 not both

Source: Bangladesh National Mathematical Olympiad 2016

February 26, 2019
Bdmocontestscontest problemnumber theorymodular arithmetic

Problem Statement

BdMO National 20162016 Higher Secondary
Problem 1: (a) Show that n(n+1)(n+2)n(n + 1)(n + 2) is divisible by 66. (b) Show that 12015+22015+32015+42015+52015+620151^{2015} + 2^{2015} + 3^{2015} + 4^{2015} + 5^{2015} + 6^{2015} is divisible by 77.
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