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National and Regional Contests
North Macedonia Contests
JBMO TST - Macedonia
2013 JBMO TST - Macedonia
5
5
Part of
2013 JBMO TST - Macedonia
Problems
(1)
equation
Source: Macedonian JBMO TST 2013
5/26/2013
Let
p
,
r
p, r
p
,
r
be prime numbers, and
q
q
q
natural. Solve the equation
(
p
+
q
+
r
)
2
=
2
p
2
+
2
q
2
+
r
2
(p+q+r)^2=2p^2+2q^2+r^2
(
p
+
q
+
r
)
2
=
2
p
2
+
2
q
2
+
r
2
.
quadratics
number theory
prime numbers
algebra
number theory proposed