MathDB
Problems
Contests
National and Regional Contests
Romania Contests
Romania National Olympiad
2014 Romania National Olympiad
1
p (2q + 1) + q (2p + 1) = 2 (p^2 + q^2) 2014 Romania NMO VII p1
p (2q + 1) + q (2p + 1) = 2 (p^2 + q^2) 2014 Romania NMO VII p1
Source:
August 15, 2024
number theory
Problem Statement
Find all primes
p
p
p
and
q
q
q
, with
p
≤
q
p \le q
p
≤
q
, so that
p
(
2
q
+
1
)
+
q
(
2
p
+
1
)
=
2
(
p
2
+
q
2
)
.
p (2q + 1) + q (2p + 1) = 2 (p^2 + q^2).
p
(
2
q
+
1
)
+
q
(
2
p
+
1
)
=
2
(
p
2
+
q
2
)
.
Back to Problems
View on AoPS