MathDB

A polynomial f(x)\equal{}ax^4\plus{}bx^3\plus{}cx^2\plus{}dx with

a,b,c,d>0

is such that

f(x)

is an integer for x \in \{ \minus{}2,\minus{}1,0,1,2 \} and f(1)\equal{}1 and f(5)\equal{}70.

(a)

Show that a\equal{}\frac{1}{24}, b\equal{}\frac{1}{4},c\equal{}\frac{11}{24},d\equal{}\frac{1}{4}.

(b)

Prove that

f(x)

is an integer for all

x \in \mathbb{Z}

Problem Statement