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even number k>46 is sum of 2 numbers whose sum of divisors is > 2n

Source: Portugal OPM 2005 p4

May 19, 2024
number theorysum of divisors

Problem Statement

A natural number nn is said to be abundant if the sum of its divisors is greater than 2n2n. For example, 1818 is abundant because the sum of its divisors, 1+2+3+6+9+181 + 2 + 3 + 6 + 9 + 18, is greater than 3636. Write every even number greater than 4646 as a sum of two numbers abundant.
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