How can I find for which X and Y the values of the polynomial
$ 100X^2+100Y^2+160X+80Y+81$
are perfect square?
Asked
Active
Viewed 409 times
1
-
Also $$(10x)^2+(10y)^2+2\cdot10x\cdot8+2\cdot10y\cdot4+8^2+4^2+1=(10x+8)^2+(10y+4)^2+1$$ – lab bhattacharjee Dec 20 '13 at 15:41
-
I think we can work modulo 4 here. – Torsten Hĕrculĕ Cärlemän Dec 20 '13 at 15:43
-
you want every x,y which satisfy your condition, don't you? – mathlove Dec 20 '13 at 15:48
-
Are $X$ and $Y$ supposed to be integers? – Mark Bennet Dec 20 '13 at 15:58
-
Yes,X and Y are integers and I am looking for every X and Y,which satisfy this condition. – Rally Dec 20 '13 at 17:43
-
See http://math.stackexchange.com/questions/435980/about-some-pythagorean-quadruples/436044#436044 where (non-complete) parametric solutions are given when the square on the right is taken to be of the form $(10t+9)^2$ – coffeemath Dec 20 '13 at 18:10