- #1

timetraveller123

- 621

- 45

## Homework Statement

let p(x) be a polynomial with integer coefficients satisfying p(0) = p(1) = 1999

show that p has no integer zeros

## Homework Equations

## The Attempt at a Solution

##

p(x) = \sum_{i= 0}^{n}{a_i x^i}

##[/B]

using the given information

a

_{0}= 1999( a prime number)

and

##

a_n + a_{n-1} ... a_1 = 0

##

then rewriting p(x)

##

p(x) = a_n(x_n + \frac{a_{n-1}}{a_n} x^{n-1} ... \frac{1999}{a_n})\\

p(x) = a_n(x-r_1)(x - r_2) ...(x - r_n)\\

##

i am hoping to do the rest of the proving by contradiction

if i assume the polynomial has integer solution then how can i disprove it