MathDB
Problems
Contests
National and Regional Contests
Mexico Contests
Mexican Girls' Contest
2022 Mexican Girls' Contest
4
4
Part of
2022 Mexican Girls' Contest
Problems
(1)
Power of 2 dividing Power of...
Source: Mexico
2/2/2022
Let
k
k
k
be a positive integer and
m
m
m
be an odd integer. Prove that there exists a positive integer
n
n
n
such that
n
n
ā
m
n^n-m
n
n
ā
m
is divisible by
2
k
2^k
2
k
.
number theory
induction