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 ].
© 1996-9 Eric W. Weisstein
1999-05-25