Question

Find all pairs (x, y) of integers such that ​

Answer 1

Step-by-step explanation:

rewrite the equation as  x3+y3-1+3xy= 6020factoring both sides we get (x+y-1)(x2+y2+1+x+y-xy) 22.5..7.43since x2+y2+1+x+y-xy= (x+y-1)2+3x+3y-3xy. now taking the above equality mode 3, we deduce thatx+y-1=2(mod 3)also x+y-1 is less than x2+y2+1+x+y-xy.so the possible values for x+y-1 are 2,5,14,20 and 35now finally by inspection we obtained that  x+y-1=20 and finally {x,y} = {18,3}or {3,18}