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composite number

Source: China south east mathematical Olympiad 2012 day1 problem 3

July 17, 2013
number theory unsolvednumber theory

Problem Statement

For composite number nn, let f(n)f(n) denote the sum of the least three divisors of nn, and g(n)g(n) the sum of the greatest two divisors of nn. Find all composite numbers nn, such that g(n)=(f(n))mg(n)=(f(n))^m (m∈N∗m\in N^*).
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