Re: how to deal with the algebra problem?

SU(2) <idyllic.bbs@xxxxxxxxxxxxxxxxxxxx> wrote:
>
> 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) ?

The b's are simply b1 * (product of prior a's), i.e.

b = b a = b a
2 1 1 1 1

b = b a = b a a
3 2 2 1 1 2

b = b a = b a a a
4 3 3 1 1 2 3
.
.
b = b a = b a a a ...a
i+1 i i 1 1 2 3 i
.
.
b = b a = b a a a ...a ...a = b
n+1 n n 1 1 2 3 i n 1

--Bill Dubuque
.