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x_i4 + 14x_ix_{i+1} + 1 = y_i^4, diophantine system

Source: Austrian - Polish 1990 APMC

May 7, 2020

system of equationsnumber theoryDiophantine equationdiophantine

Problem Statement

Find all solutions in positive integers to:

\begin{cases} x_1^4 + 14x_1x_2 + 1 = y_1^4 \\ x_2^4 + 14x_2x_3 + 1 = y_2^4 \\ ... \\ x_n^4 + 14x_nx_1 + 1 = y_n^4 \end{cases}