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Part of 1992 Austrian-Polish Competition

Problems(1)

s(n - 1)s(n)s(n + 1) is even where s(n) is sum of all positive divisors of n

Source: Austrian - Polish 1992 APMC

5/7/2020
For a natural number nn, denote by s(n)s(n) the sum of all positive divisors of n. Prove that for every n>1n > 1 the product s(nāˆ’1)s(n)s(n+1)s(n - 1)s(n)s(n + 1) is even.
SumpositiveDivisorsnumber theoryProductEven