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(360) 3

Part of 1993 Tournament Of Towns

Problems(1)

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

Source:

6/10/2024
Positive integers aa, bb and cc are positive integers with greatest common divisor equal to 11 (i.e. they have no common divisors greater than 11), and aba−b=c\frac{ab}{a-b}=c Prove that a−ba -b is a perfect square.
(SL Berlov)
number theoryPerfect SquarediophantineDiophantine equation