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Partition into two sets with equal product

Source: French TST 2004 pb.1

May 25, 2004

quadraticsmodular arithmeticnumber theorynumber theory solved

Problem Statement

n

is a positive integer, let

A = \{n,n+1,...,n+17 \}

. Does there exist some values of

n

for which we can divide

A

into two disjoints subsets

B

and

C

such that the product of the elements of

B

is equal to the product of the elements of

C