Find all x y Element zopf satisfying 1485 middot x 1745 mid

Find all x, y Element zopf satisfying 1485 middot x + 1745 middot y = 5.

Solution

1745=1485+260         ,            260=1745-1485

1485=260*6-75             ,             75 =260*6-1485=1745*6-7*1485

260=75*3+35                 ,    35=260-75*3 =1745-1485-3*(1745*6-7*1485)=-17*1745+20*1485

75=35*2+5               , 5=75-2*35=1745*6-7*1485-2*(-17*1745+20*1485)=40*1745-47*1485

5=-47*1485+40*1745

In general

5=(-47-1745n)*1485+(40+1485n)*1745

So,

x=-47-1745n

y=40+1485n

n is any integer