Thread: Diophantine Equations

Suppose the x=x0 > 0, y = y0 > 0 is a solution to x^2 - 3y^2 =6
Show that x1 = 2x0 + 3y0, y1= x0 + 2y0 is also a solution with x1 > x0 > 0, y1 > y0 >0. Can you find one solution to x^2 - 3y^2 =6 that results in there being infinitely many solutions? What would the next three solutions be in the ascent?

Suppose that is a solution to

Then, --------------(1)





{Using (1)}

Thus is also a solution with

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is a solution to

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and

and

and

and

and

and

and

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The next three solutions in the ascent are .