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(a+p)/(b+p) - a/b = 1/p^2. Find all fractions a/b (ILL 1970)

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May 22, 2011

Problem Statement

Let pp be a prime number. A rational number xx, with 0<x<10 < x < 1, is written in lowest terms. The rational number obtained from xx by adding pp to both the numerator and the denominator differs from xx by 1/p21/p^2. Determine all rational numbers xx with this property.
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