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a+b = n , x/a + y/b = 1

Source: 1995 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p3

January 27, 2020
number theory

Problem Statement

A natural number nn is called breakable if there exist positive integers a,b,x,ya,b,x,y such that a+b=na+b = n and xa+yb=1\frac{x}{a}+\frac{y}{b}= 1. Find all breakable numbers.
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