Number Theory

    

Phoenix Numbers

Authors: Walter A. Kehowski

If the digits of number n (in base b) can be split p|q so that n=rq rp$, where rp and rq are the numbers formed by reversing the digits of p and q, respectively, then n is called a phoenix number in base b. If q has k digits in base b, then n is called a k-Phoenix number in base b. For example, 1.1.n.n|b is 1-Phoenix in base b=n^2-1. The existence of infinitely many k-phoenix numbers in any base b is claimed, but not proven.

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[v1] 2026-03-11 20:50:18

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