1) Is there any way to find integer solutions for a linear equation ax+by=c, with a,b,c known and without having an another equation to substitute in the above one. ex : 3x+y=394; Is there any worst case for c being very large. 2)Is there any easy and fastest way to get t=115734564=9*(3586^2) from t1=116964=9*(12996) to "t" using the equation t=(81*x*x)+(390240*x)+116964 Actually Here if we dont know the value of "t" and searching for a perfect square using the above equation. "t" is the first perfect square we ecounter at x, and all below x cannot generate a perfect square. answer is t=280 , can we get "x" in the shortest way without substituting 1,2,3,...........280 respectively. i.e how to get from 12996 to a perfect square using the equation.