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Contests
National and Regional Contests
Bosnia Herzegovina Contests
JBMO TST - Bosnia and Herzegovina
2018 Bosnia and Herzegovina Junior BMO TST
2
2
Part of
2018 Bosnia and Herzegovina Junior BMO TST
Problems
(1)
P2 Bosnia and Herzegovina JBMO TST
Source: Bosnia and Herzegovina JBMO TST 2018
7/14/2018
Find all integer triples
(
p
,
m
,
n
)
(p,m,n)
(
p
,
m
,
n
)
that satisfy:
p
m
ā
n
3
=
27
p^m-n^3=27
p
m
ā
n
3
=
27
where
p
p
p
is a prime number.
number theory
Prime number
Diophantine equation
Exponential equation