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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Originally Posted by diddledabble Show that if and then
I forgot to add that gcd (a,b)=1 Sorry.
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
So then and then Where Is that correct?
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.
Originally Posted by diddledabble So then and then Where Is that correct?
I take back my original post. Let's try another approach.
Since gcd(a,b) = 1 then there exists integers such that
Multiply this equation by c to yield
Now where are integers
Substitute these values in equation 1) where is an integer
Thus or equivalently
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