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2021 Serbia National Math Olympiad
1
1
Part of
2021 Serbia National Math Olympiad
Problems
(1)
Interesting number theory
Source: Serbian Mathematical Olympiad 2021, P1
5/14/2021
Let
a
>
1
a>1
a
>
1
and
c
c
c
be natural numbers and let
b
≠
0
b\neq 0
b
=
0
be an integer. Prove that there exists a natural number
n
n
n
such that the number
a
n
+
b
a^n+b
a
n
+
b
has a divisor of the form
c
x
+
1
cx+1
c
x
+
1
,
x
∈
N
x\in\mathbb{N}
x
∈
N
.
number theory
Serbia