MathDB

Ax^2 + Bx + C= k x(x- 1)/2 + l x + m, integer values

Source: Eotvos 1902 p1

September 6, 2024

algebratrinomial

Problem Statement

Prove that any quadratic expression

Q(x) = Ax^2 + Bx + C

(a) can be put into the form

Q(x) = k \frac{x(x- 1)}{1 \cdot 2} + \ell x + m

where

k, \ell, m

depend on the coefficients

A,B,C

and
(b)

Q(x)

takes on integral values for every integer

x

if and only if

k, \ell, m

are integers.