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Greece Junior Math Olympiad
2023 Greece Junior Math Olympiad
4
4
Part of
2023 Greece Junior Math Olympiad
Problems
(1)
b | (a-1), (2a+1) | (5b-3), a>1
Source: Greece Junior Math Olympiad 2023 p4
3/2/2024
Find all positive integers
a
,
b
a,b
a
,
b
with
a
>
1
a>1
a
>
1
such that,
b
b
b
is a divisor of
a
−
1
a-1
a
−
1
and
2
a
+
1
2a+1
2
a
+
1
is a divisor of
5
b
−
3
5b-3
5
b
−
3
.
number theory
Divisors
divides