Making a Quadratic Function spit out Integer Outputs

blestimd4pz

blestimd4pz

Answered question

2022-03-24

Making a Quadratic Function spit out Integer Outputs for Rational Inputs
Suppose I have a quadratic function
f(x)=ax2+bx+c,       a,b,c
and I want to find rational (non-integer) values of x for which f(x)Z.

Answer & Explanation

Eve Larson

Eve Larson

Beginner2022-03-25Added 9 answers

You need to add the condition that q=±1. (I would define p,q as integers satisfying gcd(p,q)=1,q>0 and q1.) Except this, what you've done is correct.
If there are integers p,q,n,k such that a=nq and b=kqnp, then
f(pq)=nq(pq)2+(kqnp)pq+c=kp+c
is an integer.

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