Calculating the floor of y**(1/m)
2026-07-03 • Cryptography and Security
Cryptography and SecurityData Structures and Algorithms
AI summaryⓘ
The authors developed two methods using the Newton-Raphson technique to find the largest whole number whose m-th power is less than or equal to a given number y. These methods help check if y can be expressed as an integer raised to the m-th power, which is useful in number theory. Although simpler approaches like binary search exist, the authors offer alternate algorithms with this classic numerical method.
Newton-Raphson methodinteger rootfloor functionnumber theoryinteger powerbinary searchalgorithmnatural numbers
Authors
Alexandros V. Gerbessiotis
Abstract
We present two algorithms based on the Newton-Raphson method to calculate the floor of y**(1/m) for natural integer numbers y>2 and m >1. One could use such an algorithm to establish whether y is an integer power of an integer in number theory problems, even though binary search methods are traditionally considered simpler to implement.