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Netherlands Contests
Dutch BxMO/EGMO TST
2017 Dutch BxMO TST
5
square of an integer
square of an integer
Source: Netherlands TST for Bxmo 2017 problem 5
February 1, 2018
number theory
Problem Statement
Determine all pairs of prime numbers
(
p
;
q
)
(p; q)
(
p
;
q
)
such that
p
2
+
5
p
q
+
4
q
2
p^2 + 5pq + 4q^2
p
2
+
5
pq
+
4
q
2
is the square of an integer.
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