Three new simple O (n log n) time algorithms related to repeating factors are presented in
the paper. The first two algorithms employ only a basic textual data structure called the
Dictionary of Basic Factors. Despite their simplicity these algorithms not only detect
existence of powers (in particular, squares) in a string but also find all primitively rooted
cubes (as well as higher powers) and all cubic runs. Our third O (n log n) time algorithm
computes all runs and is probably the simplest known efficient algorithm for this problem. It …

Three new simple O (n log n) time algorithms related to repeating factors are presented in
the paper. The first two algorithms employ only a basic textual data structure called the
Dictionary of Basic Factors. Despite their simplicity these algorithms not only detect
existence of powers but also find all primitively rooted cubes (as well as higher powers) and
all cubic runs. Our third O (n log n) time algorithm computes all runs and is probably the
simplest known efficient algorithm for this problem. It uses additionally the Longest Common …