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Find all positive integers A which can be represented ...

Source: Romanian IMO Team Selection Test TST 1987, problem 2

September 25, 2005
modular arithmeticrationumber theory proposednumber theory

Problem Statement

Find all positive integers AA which can be represented in the form: A=(m−1n)(n−1p)(p−1m) A = \left ( m - \dfrac 1n \right) \left( n - \dfrac 1p \right) \left( p - \dfrac 1m \right) where m≥n≥p≥1m\geq n\geq p \geq 1 are integer numbers. Ioan Bogdan
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