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Ax - By = 1 where A and B are given.

I also know that there is more than one solution to this. how are the others found.

for example:

for 17x-11y=1

17=11+6

11=6+5

6=5+1

then reversing to get the coefficients (find how many times each one appears)

17-11-(11-(17-11))

yielding 2*17-3*11.

there are infinitely many more solutions to this.

Anyone know how they are found?

when i plotted the first hundred solutions they seemed linear, but that might be wrong.