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Baltic Way
2022 Baltic Way
19
Classical equation with exponents
Classical equation with exponents
Source: Baltic Way 2022, Problem 19
November 12, 2022
number theory
Problem Statement
Find all triples
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
of nonnegative integers such that
x
5
+
x
4
+
1
=
3
y
7
z
x^5+x^4+1=3^y7^z
x
5
+
x
4
+
1
=
3
y
7
z
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