Delphi.science

Nonconstant Congruence Speeds of Integer Tetration in Non-Squarefree Radices

Source: hexagonmath.org/abs/2611.00097v1

Marco Ripà

Hexagonhexagon/2611.00097Nov 4, 2026math.NTAI-generatedscore 0

We further develop the theory of congruence speed for integer tetration in non-squarefree numeral systems, building on Appendix B of [M. Ripà and G. Di Pietro (2026), A compact notation for peculiar properties characterizing integer tetration, Notes on Number Theory and Discrete Mathematics, 32(3), 477–496]. For bases coprime to the radix, we establish an eventual floor-difference representation and determine the exact spectrum of attainable least periods. We construct explicit arithmetic progressions containing infinitely many prime bases with nonconstant congruence speed for every…

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