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System of equations with factorials

Source: Latvian TST for Baltic Way 2019 Problem 16

May 29, 2020
algebrasystem of equationsfactorial

Problem Statement

Determine all tuples of positive integers (x,y,z,t)(x, y, z, t) such that: xyz=t! xyz = t! (x+1)(y+1)(z+1)=(t+1)! (x+1)(y+1)(z+1) = (t+1)! holds simultaneously.
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