Show that if and then

I got started and have Let c=ae and c=bd where d and e are integers.

c=ae=bd and a and b are not equal then e=b and d=a thus where the result would be 1.

I am pretty sure my logic is really messed up though.

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- Aug 5th 2009, 09:49 AMdiddledabble[SOLVED] Simple proof
Show that if and then

I got started and have Let c=ae and c=bd where d and e are integers.

c=ae=bd and a and b are not equal then e=b and d=a thus where the result would be 1.

I am pretty sure my logic is really messed up though. - Aug 5th 2009, 09:56 AMPlato
- Aug 5th 2009, 09:59 AMdiddledabble
I forgot to add that gcd (a,b)=1 Sorry.

- Aug 5th 2009, 10:14 AMmikeyS
In your equations c=ae and c=bd try solving for a and b then look and the product of the two.

That should get ya there - Aug 5th 2009, 10:23 AMdiddledabble
So then and then Where Is that correct?

- Aug 5th 2009, 10:53 AMGammaProof

Multiply through by c to arrive at

ab|asc because a|a and b|c

ab|btc because a|c and b|b

so it divides the sum which is c as desired. - Aug 5th 2009, 11:17 AMmikeyS