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Old 2021-07-28, 01:59   #2
Dr Sardonicus
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Feb 2017

120138 Posts

Originally Posted by bhelmes View Post
A peaceful night for you,

Let f(x)=ax²+bx+c and g(x)=Ax²+Bx+C with discriminant (f(x))=/=discr (g(x)) and f(x0)=g(x0)

I am looking for a prime p>2 where p | f(x1) and p | g(x1)

Is there a better way to calculate p than calcualting gcd [f(x), g(x)] by increasing x ?
Any such p has to divide the resultant of f(x) and g(x). If no prime factor of the resultant provides a solution, there isn't one.

EDIT: I am assuming that gcd(a, b, c) = gcd(A, B, C) = 1.

Last fiddled with by Dr Sardonicus on 2021-07-28 at 12:30 Reason: As indicated
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