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Saint Petersburg Mathematical Olympiad
2023 Saint Petersburg Mathematical Olympiad
3
NT equation
NT equation
Source: St. Petersburg 2023 10.3
August 12, 2023
number theory
Problem Statement
Find all positive integers
x
,
y
x, y
x
,
y
and primes
p
p
p
, such that
x
5
+
y
4
=
p
x
y
x^5+y^4=pxy
x
5
+
y
4
=
p
x
y
.
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