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perfect square

Source:

January 10, 2015

number theory unsolvednumber theoryKazakhstan

Problem Statement

P_k(n)

is the product of all positive divisors of

n

that are divisible by

k

(the empty product is equal to

1

). Show that

P_1(n)P_2(n)\cdots P_n(n)

is a perfect square, for any positive integer

n

.

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