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If k^3 - m^3 | km(k^2 - m^2), show that (k - m)^3 > 3km

Source: Middle European Mathematical Olympiad 2011 - Individuals I-4

September 6, 2011

number theory proposednumber theory

Problem Statement

Let

k

and

m

, with

k > m

, be positive integers such that the number

km(k^2 - m^2)

is divisible by

k^3 - m^3

. Prove that

(k - m)^3 > 3km