If the Coefficients of the Polynomial

(1) 
are specified to be Integers, then integral Roots must have a Numerator which is a
factor of and a Denominator which is a factor of (with either sign possible). This follows since a
Polynomial of Order with integral Roots can be expressed as

(2) 
where the Roots are
,
, ..., and
. Factoring out the
s,

(3) 
Now, multiplying through,

(4) 
where we have not bothered with the other terms. Since the first and last Coefficients are and
, all the integral roots of (1) are of the form [factors of ]/[factors of ].
© 19969 Eric W. Weisstein
19990525