On Integral Basis of Pure Number Fields

Let K=Q(√[n]a) be an extension of degree n of the field of rational numbers, where the integer a is such that for each prime p dividing n either p a or the highest power of p dividing a is coprime to p; this condition is clearly satisfied when $a, n$ are coprime or a is squarefree. The present paper gives explicit construction of an integral basis of K along with applications. This construction of an integral basis of K extends a result proved in [J. Number Theory, {173} (2017), 129-146] regarding periodicity of integral bases of Q(√[n]a) when a is squarefree.