Help on solution for v^2-b=a*x^2

jtavares · 2005-03-17, 20:04

How to solve ? - find integers v and x such that

v*v - b = a*x*x

where a and b are known and not perfect squares.

R.D. Silverman · 2005-03-17, 20:23

Quote:

Originally Posted by jtavares

How to solve ? - find integers v and x such that

v*v - b = a*x*x

where a and b are known and not perfect squares.

This is just an extension of the Pell Equation. It has been completely solved.
Just do a Web search.

Note that b needs to split in the quadratic field Q(sqrt(a))

alpertron · 2005-03-17, 20:31

Just go to my Quadratic Diophantine Equation Solver. It has a step by step mode that shows you how it finds the solutions.

jtavares · 2005-03-17, 20:47

Thanks.

So it seems to me that there is no need to factor a and b.
Since when a is equal to 1 v*v - b = x*x can be solved by factoring b - Fermat factorization method.

2005-03-17, 20:04	#1
jtavares Nov 2004 1001₂ Posts	*Help on solution for v^2-b=ax^2** How to solve ? - find integers v and x such that vv - b = axx where a and b are known and not perfect squares. Last fiddled with by jtavares on 2005-03-17 at 20:08*

2005-03-17, 20:47	#4
jtavares Nov 2004 9₁₀ Posts	Thanks. So it seems to me that there is no need to factor a and b. Since when a is equal to 1 vv - b = xx can be solved by factoring b - Fermat factorization method. Last fiddled with by jtavares on 2005-03-17 at 20:49

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2005-03-17, 20:31	#3
alpertron Aug 2002 Buenos Aires, Argentina 556₁₆ Posts	Just go to my Quadratic Diophantine Equation Solver. It has a step by step mode that shows you how it finds the solutions.