Find complete set of integer solutions
Find the complete set of integer solutions in x and y to
821x + 1997y = 24047:
Determine all solutions with x > 0 and y > 0.
I started by finding the GCD(821, 1997)=1
Then I went backwards using the Euclidean algorithm and found 1=821(90)-1997(37).
So we have a particular solution xo=90, y0=-37.
Our particular solution is x0=24047*90=216630 and y0=24047*-37=-889,739.
then I have:
x=216,630+1997t and y=-889,739-821t.
Now it's the final part of determining all solutions with x>0 and y>0 that's getting me.