2014/01/21 by A. A. Grinberg, Grinberg, Anatoly A., Luryi, Serge
Computer Science · Mathematics · #11A99 #Cryptography and Residue Arithmetic #FOS: Mathematics #General Mathematics (math.GM) #Mathematics and Applications #Numerical Methods and Algorithms #math.GM #msc:11A99
paper · pdf · doi:10.48550/arxiv.1401.5486
9 pages (v2): added Appendix with a simplified derivation of the main result; no other changes
openalex publication_date 2014/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We believe we have made progress in the age-old problem of divisibility rules for integers. Universal divisibility rule is introduced for any divisor in any base number system. The divisibility criterion is written down explicitly as a linear form in the digits of the test number. The universal criterion contains only two parameters that depend on the divisor and are easily calculated. These divisibility parameters are not unique for a given divisor but each two-parameter set yields a unique criterion. Well-known divisibility rules for exemplary divisors in the decimal system follow from the universal expression as special cases.