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c = a + b/a -1/b is perfect square.

Source: New Zealand NZMOC Camp Selection Problems 2013 p8

September 19, 2021

Perfect Squarenumber theory

Problem Statement

Suppose that

a

and

b

are positive integers such that

c = a +\frac{b}{a} -\frac{1}{b}

is an integer. Prove that

c

is a perfect square.