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2022 APMO
1
Pair of multiples
Pair of multiples
Source: APMO 2022 P1
May 17, 2022
number theory
APMO
APMO 2022
divisible
multiple
Hi
Problem Statement
Find all pairs
(
a
,
b
)
(a,b)
(
a
,
b
)
of positive integers such that
a
3
a^3
a
3
is multiple of
b
2
b^2
b
2
and
b
−
1
b-1
b
−
1
is multiple of
a
−
1
a-1
a
−
1
.
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