OK: long story short, restrictions are positive integers - the book gives us 63x+7=23y

so I start:

63 = (-23)(-2) + 17

-23 = 17(-1) + (-6)

17 = (-6)(-2) + 5

-6 = (5)(-1) + (-1)

5 = (-1)(-5) + 0

so gcd(63,-23)=-1

does this work? I mean with the whole negative thing? because I continue on like that and eventually get:

x = 28 + 23t

y = 77 + 63t

where t>0

then I get, t>(-28/23) and t>(-77/63)

and I'm stuck. Because it has to be positive - and it has to be an integer

therefore - i think it has to do with the negatives - how would one go about them?