Find all x y Z satisfying 1485 middot x 1745 middot y 5Sol

Find all x, y Z 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=20*1485-17*1745

75=35*2+5                ,            5 = 75-2*35=40*1745-47*1485

5=40*1745-47*1485

IN general

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

So general x,y is

x=-47-1745n, y=40+1485n, n is any integer