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2008 PUMaC Number Theory A8 / B9
Source:
October 4, 2019
number theory
Problem Statement
Find all sets of three primes
p
,
q
p, q
p
,
q
, and
r
r
r
such that
p
+
q
=
r
p + q = r
p
+
q
=
r
and
(
r
−
p
)
(
q
−
p
)
−
27
p
(r -p)(q - p) - 27p
(
r
−
p
)
(
q
−
p
)
−
27
p
is a perfect square.
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