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Junior Balkan MO
2022 Junior Balkan Mathematical Olympiad
3
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2022 Junior Balkan Mathematical Olympiad
Problems
(1)
2022 Junior Balkan MO, Problem 3
Source: 2022 JBMO Problem 3
6/30/2022
Find all quadruples of positive integers
(
p
,
q
,
a
,
b
)
(p, q, a, b)
(
p
,
q
,
a
,
b
)
, where
p
p
p
and
q
q
q
are prime numbers and
a
>
1
a > 1
a
>
1
, such that
p
a
=
1
+
5
q
b
.
p^a = 1 + 5q^b.
p
a
=
1
+
5
q
b
.
number theory
prime numbers
Diophantine equation
JBMO