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2011 Greece Junior Math Olympiad
3
3
Part of
2011 Greece Junior Math Olympiad
Problems
(1)
Number Theory
Source: Archimedes Junior 2011
3/16/2020
If the number
3
n
+
1
3n +1
3
n
+
1
, where n is integer, is multiple of
7
7
7
, find the possible remainders of the following divisions: (a) of
n
n
n
with divisor
7
7
7
, (b) of
n
m
n^{m}
n
m
with divisor
7
7
7
, for all values of the positive integer
m
,
m
>
1
m, m >1
m
,
m
>
1
.
number theory