GAPS BETWEEN DIVISIBLE TERMS IN

Characterizing the Multiplicative Group of a Real Closed Field in Terms of its Divisible Maximal Subgroup

The Terms in Lucas Sequences Divisible by Their Indices

For Lucas sequences of the first kind (un)n≥0 and second kind (vn)n≥0 defined as usual by un = (α n − βn)/(α − β), vn = α n + βn, where α and β are either integers or conjugate quadratic integers, we describe the sets {n ∈ N : n divides un} and {n ∈ N : n divides vn}. Building on earlier work, particularly that of Somer, we show that the numbers in these sets can be written as a product of a so...

Terms in Elliptic Divisibility Sequences Divisible by Their Indices

Let D = (Dn)n≥1 be an elliptic divisibility sequence. We study the set S(D) of indices n satisfying n | Dn. In particular, given an index n ∈ S(D), we explain how to construct elements nd ∈ S(D), where d is either a prime divisor of Dn, or d is the product of the primes in an aliquot cycle for D. We also give bounds for the exceptional indices that are not constructed in this way.

a cross-comparative dtudy between two textbook series in terms of the presentation of politeness

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characterizing the multiplicative group of a real closed field in terms of its divisible maximal subgroup