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2020 PUMaC Combinatorics A8

Source:

January 1, 2022

combinatorics

Problem Statement

Let

f(k)

denote the number of triples

(a, b, c)

of positive integers satisfying

(k + 1)

with

(k - 1)

not dividing

a, k

not dividing

b

, and

(k + 1)

not dividing

c

. Find the product of all integers

k

in the range 3 \le k \le 20 such that

(k + 1)

divides

f(k)

.

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