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National and Regional Contests
Switzerland Contests
Switzerland - Final Round
2013 Switzerland - Final Round
9
9
Part of
2013 Switzerland - Final Round
Problems
(1)
p^m - q^3 = n^3
Source: Switzerland - 2013 Swiss MO Final Round p9
1/14/2023
Find all quadruples
(
p
,
q
,
m
,
n
)
(p, q, m, n)
(
p
,
q
,
m
,
n
)
of natural numbers such that
p
p
p
and
q
q
q
are prime and the the following equation is fulfilled:
p
m
ā
q
3
=
n
3
p^m - q^3 = n^3
p
m
ā
q
3
=
n
3
number theory
diophantine
Diophantine equation