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SIMULTANEOUS NIVEN NUMBERS IN ARITHMETIC PROGRESSIONS FOR POWER-RELATED BASES
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- Bulletin of the Australian Mathematical Society , First View
- Published online by Cambridge University Press:
- 21 April 2026, pp. 1-10
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Recently, Harrington et al. [‘Every arithmetic progression contains infinitely many b-Niven numbers’, Bull. Aust. Math. Soc. 109(3) (2024), 409–413] proved that every arithmetic progression contains infinitely many base-b Niven numbers for any fixed
$b\ge 2$. We use a sparse repunit construction to treat a structured two-base version of the same problem, showing that every arithmetic progression with common difference relatively prime to b contains infinitely many integers that are simultaneously b-Niven and 
$b^k$-Niven (indeed, we can obtain simultaneous 
$b^\ell $-Niven-ness for 
$\ell =1,\ldots , k$).
Repunit Lehmer numbers
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 54 / Issue 1 / February 2011
- Published online by Cambridge University Press:
- 28 October 2010, pp. 55-65
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