MathDB
xy=- 1 (mod z), yz = 1 (mod x), zx = 1 (mod y).

Source: Austrian Polish 1991 APMC

May 1, 2020
number theorysystem of equations

Problem Statement

Consider the system of congruences {xy≡−1  (modz)yz≡1  (modx)zx≡1  (mody)\begin{cases} xy \equiv - 1 \,\, (mod z) \\ yz \equiv 1 \, \, (mod x) \\zx \equiv 1 \, \, (mod y)\end {cases} Find the number of triples (x,y,z)(x,y, z) of distinct positive integers satisfying this system such that one of the numbers x,y,zx,y, z equals 1919.
Back to ProblemsView on AoPS