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4
Power of 2 dividing Power of...
Power of 2 dividing Power of...
Source: Mexico
February 2, 2022
number theory
induction
Problem Statement
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
.
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