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3 rational numbers in arithmetic progression, system

Source: Vietnam MO 1978 P4

July 29, 2018

arithmetic sequencesystem of equationsalgebra

Problem Statement

Find three rational numbers

\frac{a}{d}, \frac{b}{d}, \frac{c}{d}

in their lowest terms such that they form an arithmetic progression and

\frac{b}{a} =\frac{a + 1}{d + 1}, \frac{c}{b} = \frac{b + 1}{d + 1}