Can you Solve this? | Math Olympiad 

Ill-posed problem. General (infinite) solution in the reals: all the points (x,y = ±√(x^2 - 39)) with |x|≥√39 Infinite solutions can also be given in complex numbers

Yes , I solved it in my mind within 30 seconds 8^2 - 5^2 64 - 25 = 39

You say solve the "Math Olympiad problem" but then magically make it so that x-y

Say that x,y are positive integers.Otherwise there are many solutions

I learned this method from you, thank you! , x^2-y^2=39*1 , (x+y)(x-y)=39*1 , let x+y=39 , let x-y=1 , x+y+x-y=39+1 , 2x=40 , x=20 , y=x-1 , y=20-1 , y=19 , test , 20^2-19^2=400-361 , 400-361=39 , OK , --> , 39= 3*13 , 13*3 , 1*39 , x^2-y^2=13*3 , (x+y)(x-y)=13*3 , let x+y=13 , let x-y=3 , x+y+x-y=13+3 , 2x=16 , x=8 , y=x-3 , y=8-3 , y=5 , test , 8^2-5^2=64-25 , 64-25=39 , OK , x^2-y^2=3*13 , (x+y)(x-y)=3*13 , let x+y=3 , let x-y=13 , x+y+x-y=3+13 , 2x=16 , x=8 , y=x-13 , y=8-13 , y= -5 , test , 8^2-(-5)^2=64-25 , 64-25=39 , OK , x^2-y^2=1*39 , (x+y)(x-y)=1*39 , let x+y=1 , let x-y=39 , x+y+x-y=1+39 , 2x=40 , x=20 , y=1-20 , y= -19 , test , 20^2-(-19)^2=400-361 , 400-361=39 , OK ,