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8
2023 Algebra/NT #8: Clean bijective NT sum
2023 Algebra/NT #8: Clean bijective NT sum
Source:
November 27, 2023
floor function
number theory
Problem Statement
Let
S
S
S
be the set of ordered pairs
(
a
,
b
)
(a, b)
(
a
,
b
)
of positive integers such that
gcd
(
a
,
b
)
=
1
\gcd(a, b) = 1
g
cd
(
a
,
b
)
=
1
. Compute
∑
(
a
,
b
)
∈
S
⌊
300
2
a
+
3
b
⌋
.
\sum_{(a, b) \in S} \left\lfloor \frac{300}{2a+3b} \right\rfloor.
(
a
,
b
)
∈
S
∑
⌊
2
a
+
3
b
300
⌋
.
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