Question

2020^a+b^2022=2022^c

Aflati numerele naturale a,b,c

Answer 1

Presupunem ca $c\neq 0.$ Atunci, avem ca $3\mid 2022^c$ deci $3\mid 2020^a+b^{2022}.$

Dar $2020^a\equiv 1\pmod{3}$ iar $b^{2022}\equiv 1\text{ sau }0\pmod{3}$ deci $3\nmid 2020^a+b^{2022}$ contradictie.

Prin urmare, $c=0$ ceea ce implica $a=0$ si $b=0.$