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USA - Middle School Tournaments
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2020 LMT Spring
27
Spring 2020 Team Round Problem 27
Spring 2020 Team Round Problem 27
Source:
August 22, 2020
Problem Statement
Let
S
n
=
∑
k
=
1
n
(
k
5
+
k
7
)
.
S_n=\sum_{k=1}^n (k^5+k^7).
S
n
=
∑
k
=
1
n
(
k
5
+
k
7
)
.
Let the prime factorization of
gcd
(
S
2020
,
S
6060
)
\text{gcd}(S_{2020},S_{6060})
gcd
(
S
2020
,
S
6060
)
be
p
1
k
1
⋅
p
2
k
2
⋯
p
i
k
i
p_1^{k_1}\cdot p_2^{k_2}\cdots p_i^{k_i}
p
1
k
1
⋅
p
2
k
2
⋯
p
i
k
i
. Compute
p
1
+
p
2
+
⋯
+
p
i
+
k
1
+
k
2
+
⋯
+
k
i
p_1+p_2+\cdots +p_i+k_1+k_2+\cdots + k_i
p
1
+
p
2
+
⋯
+
p
i
+
k
1
+
k
2
+
⋯
+
k
i
.
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