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Problems
Contests
National and Regional Contests
Mexico Contests
Regional Olympiad of Mexico Center Zone
2012 Regional Olympiad of Mexico Center Zone
5
5
Part of
2012 Regional Olympiad of Mexico Center Zone
Problems
(1)
A cool sum
Source: Mexico Regional Contest 2012-Problem 5
9/13/2015
Consider and odd prime
p
p
p
. For each
i
i
i
at
{
1
,
2
,
.
.
.
,
p
−
1
}
\{1, 2,..., p-1\}
{
1
,
2
,
...
,
p
−
1
}
, let
r
i
r_i
r
i
be the rest of
i
p
i^p
i
p
when it is divided by
p
2
p^2
p
2
. Find the sum:
r
1
+
r
2
+
.
.
.
+
r
p
−
1
r_1 + r_2 + ... + r_{p-1}
r
1
+
r
2
+
...
+
r
p
−
1
fermat's little theorem
number theory