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Turkey Team Selection Test
2017 Turkey Team Selection Test
1
Turkey TST Number Theory
Turkey TST Number Theory
Source: Turkey Team Selection Test 2017 P1
June 1, 2017
number theory
Problem Statement
m
,
n
m, n
m
,
n
are positive integers and
p
p
p
is a prime number. Find all triples
(
m
,
n
,
p
)
(m, n, p)
(
m
,
n
,
p
)
satisfying
(
m
3
+
n
)
(
n
3
+
m
)
=
p
3
(m^3+n)(n^3+m)=p^3
(
m
3
+
n
)
(
n
3
+
m
)
=
p
3
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