MODULAR ARITHMETIC OF ITERATED POWERS Academic Article uri icon

abstract

  • To give examples of large combinatorial problems D. Knuth modified W. Ackermann's example of a recursive, but not primitive recursive, function to produce a class of nonassociative compositions. These arrow compositions, which we call krata, are defined on the positive integers by settingB1T=BTBD1=BBD+1(T+1)=BD(BD+1T).The function k(B, D, T) = BDT, which usually takes on large values, has interesting periodicity properties modulo every positive integer M. For fixed B, D, T 2 the sequences {BDn}, {BnT} and {Bnn} are eventually constant modulo M. Also {nDT}, {nDn}, {nnT} and {nnn} are eventually periodic modulo M. An algorithm for calculating BDT modulo M is given. 1983.

published proceedings

  • COMPUTERS & MATHEMATICS WITH APPLICATIONS

altmetric score

  • 2.5

author list (cited authors)

  • BLAKLEY, G. R., & BOROSH, I.

citation count

  • 3

complete list of authors

  • BLAKLEY, GR||BOROSH, I

publication date

  • January 1983