Today, we shall embark on a quest to tame one of the greatest equations in history – x² – dy² = 1.
Some may view this as an mere ordinary equation but for me, it has taken hours of sweat and passion to tame this equation and launch a solution to this equation.
let us examine the equation = x² – dy² = 1
this can be simplified down to (x – y√d)(x + y√d) = 1:
Now here comes the ingenious part – squaring both the sides of the equation will not change the fundamental equation( as 1² = 1) but the following equation can be denoted as the following:
(x – y√d)²(x+y√d)²= 1
=> ((x² + dy²) -2xy√d)((x² + dy²) +2xy√d) = 1 thus we have obtained a new set of equations precisely due to the property that 1 multiplied by any number yields 1.
numberdot 