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Mathematical Excellence Olympiad
2019 IMEO
5
5
Part of
2019 IMEO
Problems
(1)
Interesting divisibility condition on exponential expressions
Source: IMEO 2019, Problem 5
10/14/2019
Find all pairs of positive integers
(
s
,
t
)
(s, t)
(
s
,
t
)
, so that for any two different positive integers
a
a
a
and
b
b
b
there exists some positive integer
n
n
n
, for which
a
s
+
b
t
∣
a
n
+
b
n
+
1
.
a^s + b^t | a^n + b^{n+1}.
a
s
+
b
t
∣
a
n
+
b
n
+
1
.
Proposed by Oleksii Masalitin (Ukraine)
number theory
number theory proposed
Divisibility