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IMO Longlists
1985 IMO Longlists
54
54
Part of
1985 IMO Longlists
Problems
(1)
Find gcd(S_{n} , S_{3n})
Source:
9/13/2010
Set
S
n
=
∑
p
=
1
n
(
p
5
+
p
7
)
S_n = \sum_{p=1}^n (p^5+p^7)
S
n
=
∑
p
=
1
n
(
p
5
+
p
7
)
. Determine the greatest common divisor of
S
n
S_n
S
n
and
S
3
n
.
S_{3n}.
S
3
n
.
number theory
greatest common divisor
induction
algorithm
modular arithmetic
algebra
binomial theorem