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12^x + 13^y - 14^z = 2013^t diophantine in positive integers

Source: Balkan MO Shortlist 2013 N3 BMO

March 9, 2020
Diophantine equationdiophantinenumber theory

Problem Statement

Determine all quadruplets (x,y,z,tx, y, z, t) of positive integers, such that 12x+13yāˆ’14z=2013t12^x + 13^y - 14^z = 2013^t.