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2023 Poland - Second Round
1
1
Part of
2023 Poland - Second Round
Problems
(1)
Find all b's
Source: Polish Math Olympiad 2023 2nd stage P1
2/10/2023
Find all positive integers
b
b
b
with the following property: there exists positive integers
a
,
k
,
l
a,k,l
a
,
k
,
l
such that
a
k
+
b
l
a^k + b^l
a
k
+
b
l
and
a
l
+
b
k
a^l + b^k
a
l
+
b
k
are divisible by
b
k
+
l
b^{k+l}
b
k
+
l
where
k
≠
l
k \neq l
k
=
l
.
number theory
Divisibility