Explicit integral basis of [formula omitted

Abstract

Let p1,p2 be distinct prime numbers and K=Q(θ) be an algebraic number field with θ satisfying an irreducible polynomial xp1p2−a over the field Q of rationals. In this article, we provide an explicit p-integral basis of K for each prime p. These p-integral bases lead to the construction of an integral basis of K which is illustrated with examples. As an application, we show that when a is squarefree integer such that api−1≢1modpi2 for each i, i=1,2, then K has a power basis.