how to deal with the algebra problem?

From: idyllic.bbs@xxxxxxxxxxxxxxxxxxxx (SU(2))
Date: 16 Apr 2005 12:57:19 GMT

assume a1*a2*...*an=1
does there exist b1,b2,...,bn such that:
a1(b1/b2)=1
a2(b2/b3)=1
.
.
.
an(bn/b1)=1

if exist, how to find these bi (i=1~n) ?

thanks in advance.

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