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2017 IMAR Test
2
Sum of residues
Sum of residues
Source: IMAR 2017, problem 2
November 18, 2017
number theory
abstract algebra
Problem Statement
For every
k
≤
n
k\leq n
k
≤
n
define
r
k
r_k
r
k
the residue of
2
n
2^n
2
n
modulo
k
k
k
. Prove that
∑
r
i
>
n
∗
l
o
g
2
(
n
3
)
2
−
n
\sum r_i> \frac{n*log_2(\frac{n}{3})}{2}-n
∑
r
i
>
2
n
∗
l
o
g
2
(
3
n
)
−
n
, for any
n
≥
2
n\geq 2
n
≥
2
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