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Baltic Way 2022 · Problem 19

Number Theory

Find all triples (x,y,z)(x,y,z) of nonnegative integers such that

x5+x4+1=3y7z.x^5+x^4+1=3^y7^z.
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Topics

Diophantine equations

Solutions

No verified local solution is currently available.

Contest context

Results from Baltic Way 2022

10 teams

Mean score
2.4 / 5
Scores of 4 or 5
5 / 10
Estonia
5 / 5

Score distribution

03
11
21
30
44
51
All team scores
TeamScore
Poland4 / 5
Germany4 / 5
Lithuania4 / 5
Estonia5 / 5
Denmark0 / 5
Latvia4 / 5
Sweden2 / 5
Norway1 / 5
Finland0 / 5
Iceland0 / 5