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(S(n))^3 <n^4 for sum of all different natural divisors of odd natural n>1

Source: 1998 Belarus TST 3.1

December 25, 2020

inequalitiesnumber theorySumDivisors

Problem Statement

Let

S(n)

be the sum of all different natural divisors of odd natural number

n> 1

(including

n

and

1

). Prove that

(S(n))^3 <n^4