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4
2013 PUMaC Number Theory A4/B6
2013 PUMaC Number Theory A4/B6
Source:
November 24, 2013
modular arithmetic
greatest common divisor
Problem Statement
Let
d
d
d
be the greatest common divisor of
2
3
0
10
−
2
2^{30^{10}}-2
2
3
0
10
−
2
and
2
3
0
45
−
2
2^{30^{45}}-2
2
3
0
45
−
2
. Find the remainder when
d
d
d
is divided by
2013
2013
2013
.
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