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.
The polynomial is irreducible over the integers but none of the criteria above can be applied on this polynomial.