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Problem 4 of Second round - Injective function with perfect squares property

Source: VI International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

December 19, 2019
number theoryinjective functionfunction

Problem Statement

Let kk be a natural number. For each natural number nn we define fk(n)f_k (n) to be the least number, greater than knkn, for which nfk(n)nf_k (n) is a perfect square. Prove that fk(n)f_k (n) is injective.
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