Is it true that polynomials of the form :
where , , is odd number , , and
are irreducible over the ring of integers ?
Note that general form of is : , so condition is equivalent to the condition . Also polynomial can be rewritten into form :
Eisenstein's criterion , Cohn's criterion , and Perron's criterion cannot be applied to the polynomials of this form.
Example :
The polynomial is irreducible over the integers but none of the criteria above can be applied on this polynomial.