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TOT 360 1993 Spring O J3 (a -b) perfect square if ab/(a-b)=c

Source:

June 10, 2024

number theoryPerfect SquarediophantineDiophantine equation

Problem Statement

Positive integers

a

b

and

c

are positive integers with greatest common divisor equal to

1

(i.e. they have no common divisors greater than

1

), and

\frac{ab}{a-b}=c

Prove that

a -b

is a perfect square.
(SL Berlov)