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p/a+p/b=1, p|a+b

Source: Assara 2024 J2

October 14, 2024
number theoryprime numbers

Problem Statement

Let pp be a prime number. Positive integers numbers aa and bb are such pa+pb=1\frac{p}{a}+\frac{p}{b}=1 and a+ba+b is divisible by pp. What values can an expression a+bp\frac{a+b}{p} take? Yu.A.Karpenko
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