Math Forum Discussions

Scott Berg

Posts: 1,260
Registered: 12/12/04

Re: ----- ----- -- Solutions of an equation
Posted: Mar 20, 2013 5:32 PM

Plain Text

"Deep" <deepkdeb@yahoo.com> wrote in message
news:05d6d36b-17b5-4be4-8abd-8b8147c1e17b@googlegroups.com...
>
> Consider (1) below under the given conditions:
>
> XY = AB (1)
>
> Conditions: X, Y, A, B are odd integers each > 1.
> The symbol (m, n) = 1 means m, n are coprime odd integers each > 1.
> Example m = 3, n = 35.
> (X, Y) = 1, (A, B) = 1
>
> Statement:: Given (1) one gets:
>
> X = A and Y = B (2) or
>
> X = a and Y = b (3) where AB = ab, (a, b) = 1
>
> Any valid comment upon the correctness of the Statement will be
> appreciated.
>
> Deep

rearranging;

XY = AB

X = A and Y = B (obvious, above condition does not apply) (2)
or

X = a and Y = b (3) where AB = ab, (a, b) = 1

the (a, b) = 1 does not need to follow as it is correct without the
condition.