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Macedonia National Olympiad
2013 Macedonia National Olympiad
1
Problem 1
Problem 1
Source: Macedonian National Olympiad 2013
April 6, 2013
modular arithmetic
number theory proposed
number theory
Problem Statement
Let
p
,
q
,
r
p,q,r
p
,
q
,
r
be prime numbers. Solve the equation
p
2
q
+
q
2
p
=
r
p^{2q}+q^{2p}=r
p
2
q
+
q
2
p
=
r
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