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Soros Olympiad in Mathematics
VI Soros Olympiad 1999 - 2000 (Russia)
11.4
p^{2k}+q^{2n}=r^2 (VI Soros Olympiad 1990-00 R2 11.4)
p^{2k}+q^{2n}=r^2 (VI Soros Olympiad 1990-00 R2 11.4)
Source:
May 28, 2024
number theory
Diophantine equation
diophantine
Problem Statement
For prime numbers
p
p
p
and
q
q
q
, natural numbers
n
n
n
,
k
k
k
,
r
r
r
, the equality
p
2
k
+
q
2
n
=
r
2
p^{2k}+q^{2n}=r^2
p
2
k
+
q
2
n
=
r
2
holds. Prove that the number
r
r
r
is prime.
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