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In this paper we study the factorization of the polynomials 1+x^(2^n)over a field K, which have the same form as the Fermat numbers . As we notice that 1+x^(2^n) is equal to the 2^(n+1)th cyclotomic p...
In this paper we study the factorization of the p^(n+1)th cyclotomic polynomials Qp^(n+1)(x) over a field K for prime p>2 and integer n>=0. Our methodology to solve the problem is due to some conclusi...
In this article, we studied the order of an integer q modulo integer m, and then studied the factorization of the mth cyclotomic polynomial over a field K. We discussed the order of q modulo m by the ...
Let Qm(x) be the mth cyclotomic polynomial over finite field Fq. The factorization of Qm(x^t) and f(x^t) over Fq are discussed, where t is an positive integer larger than one and f(x) is any irreducib...
Let An denote the height of cyclotomic polynomial Φn,where n is a product of k distinct odd primes. We prove that An "k'(n)k−12k−1 −1 with −log "k  c2k, c > 0. The same state...
We study the explicit factorization of $2^n r$-th cyclotomic polynomials over finite field $\mathbb{F}_q$ where $q, r$ are odd with $(r, q) =1$. We show that all irreducible factors of $2^n r$-th cyc...

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