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Sweden Contests
Swedish Mathematical Competition
2014 Swedish Mathematical Competition
6
6
Part of
2014 Swedish Mathematical Competition
Problems
(1)
find odd primes p,q such that x^p + y^q = pq has >=1 solution
Source: 2014 Swedish Mathematical Competition p6
4/30/2021
Determine all odd primes
p
p
p
and
q
q
q
such that the equation
x
p
+
y
q
=
p
q
x^p + y^q = pq
x
p
+
y
q
=
pq
at least one solution
(
x
,
y
)
(x, y)
(
x
,
y
)
where
x
x
x
and
y
y
y
are positive integers.
number theory
diophantine
Diophantine equation