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Switzerland Contests
Switzerland - Final Round
2015 Switzerland - Final Round
2
Number Theory
Number Theory
Source: Swiss NMO D1 P2
November 28, 2015
number theory
Problem Statement
Find all pairs
(
m
,
p
)
(m,p)
(
m
,
p
)
of natural numbers , such that
p
p
p
is a prime and
2
m
p
2
+
27
2^mp^2+27
2
m
p
2
+
27
is the third power of a natural numbers
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