Post a New Question


posted by .

What is the largest value of d, such that for some degree d polynomial f(x) with integer coefficients, |f(x)|=1024 for more than d integer values of x?

  • algebra -

    If we let
    f(x) = (k1 x-r1)(k2 x-r2)...(kn x-rn)
    then (r1/k1)(r2/k2)...(rn/kn) = 1024/1

    Now, 1024 = 2^10, so all the k's are 1, and all the r's multiplied together are 2^10

    the possible distinct roots are
    so, f(x) = (x-2)(x-4)(x-8)(x-16) + 1024
    has 4 values of x such that f(x) = 1024.

    I'd say 3 is the max d such that there are n>d places where f(x) = 1024

    If I'm way off base here, let me know. I'd be interested in how it's supposed to be done. What are you studying in the class now?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

More Related Questions

Post a New Question