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A note on divisibility sequences

Ward, Morgan (1939) A note on divisibility sequences. Bulletin of the American Mathematical Society, 45 (4). pp. 334-336. ISSN 0002-9904. doi:10.1090/s0002-9904-1939-06980-2.

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A sequence of rational integers (u): u₀, u₁, u₂, . . .u_n, . . . is called a divisibility sequence if u_r divides u_s whenever r divides s, and any integer M dividing terms of (u) with positive suffix is called a divisor of (u). The suffix s is called a rank of apparition of M if u_s ≡ 0 (mod M), but u_r /≡ (mod M) if r is a proper divisor of s. It follows from a previous note of mine in this Bulletin (Ward [l]) that a necessary and sufficient condition that every divisor of (u) shall have only one rank of apparition is that (u) have the following property.

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Additional Information:© 1939 American Mathematical Society. Presented to the Society, February 25, 1939.
Issue or Number:4
Record Number:CaltechAUTHORS:20200408-154922593
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:102415
Deposited By: Tony Diaz
Deposited On:08 Apr 2020 23:00
Last Modified:16 Nov 2021 18:11

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