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.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Solutions to a linear equation and perfect square

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