The rational root theorem states that, if a rational number
(where
and
are relatively prime) is a root of a polynomial with integer coefficients, then
is a factor of the constant term and
is a factor of the leading coefficient. In other words, for the polynomial,
, if
, (where
and
) then
and
Let
, where
.
Assume
for coprime
. Therefore,
Let
Thus,
As
is coprime to
and
, thus
.
Again,
Let
Thus,
As
is coprime to
and
, thus
.
For
, if
, (where
and
) then
and
. [Proved]