generalized to sequences with values in any ring where the concept of divisibility is defined. A strong divisibility sequence is an integer sequence ( a n )...

In mathematics, an elliptic divisibility sequence (EDS) is a sequence of integers satisfying a nonlinear recursion relation arising from division polynomials...

preserving divisibility by the divisor of interest. Therefore, unless otherwise noted, the resulting number should be evaluated for divisibility by the same...

Thus the Fibonacci sequence is an example of a divisibility sequence. In fact, the Fibonacci sequence satisfies the stronger divisibility property gcd ( F...

1 {\displaystyle (U_{m}(P,Q))_{m\geq 1}} is a strong divisibility sequence. Other divisibility properties are as follows: If n is an odd multiple of...

units −1 and 1 and prime numbers have no non-trivial divisors. There are divisibility rules that allow one to recognize certain divisors of a number from the...

results in a Fibonacci prime). That is to say, the Fibonacci sequence is a divisibility sequence. Fp is prime for 8 of the first 10 primes p; the exceptions...

5, 6, 7, 8, 10, 12, 13, 18, 30). Lucas and Lehmer sequences are examples of divisibility sequences. It is also known that if ( W n ) n ≥ 1 {\displaystyle...

any m and n. That is, the repunits of a fixed base form a strong divisibility sequence. As a consequence, If m and n are relatively prime, Rm(b) and Rn(b)...

after receiving his doctorate. The sequence of numbers involved is sometimes referred to as the hailstone sequence, hailstone numbers or hailstone numerals...

that bn − 1 is divisible by all digit sums in the sequence, then the divisibility by those sums is maintained. If our initial sequence is chosen so that...

strana), a Czech political party Electrodynamic suspension Elliptic divisibility sequence Energy-dispersive X-ray spectroscopy Effluent decontamination system...

aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches...

Every sequence of digits, in any base, is the sequence of initial digits of some factorial number in that base. Another result on divisibility of factorials...

linear recurrence sequence, linear-recursive sequence, linear-recurrent sequence, or a C-finite sequence. For example, the Fibonacci sequence 0 , 1 , 1 , 2...

The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while researching...

theorem Congruent number Arithmetic of abelian varieties Elliptic divisibility sequences Mordell curve Fermat's Last Theorem Mordell conjecture Euler's sum...

repdigit in tredecimal (11113). 183 is the fourth element of a divisibility sequence 1 , 3 , 13 , 183 , … {\displaystyle 1,3,13,183,\dots } in which...

ace of divisibility. The more divisible a number is ... the more useful it proves in certain situations. ... Is it because 60 is highly divisible that the...

Miniworkshop: Hilbert's Tenth Problem, Mazur's Conjecture and Divisibility Sequences (PDF). MFO Report. Vol. 3. Mathematisches Forschungsinstitut Oberwolfach...

Press, ISBN 978-0-19-533454-8 Koshy, Thomas & Zhenguang Gao (2011) "Some divisibility properties of Catalan numbers", Mathematical Gazette 95:96–102. Larcombe...

is divisible by the sum of its digits (which is b). No self-descriptive number can be a prime number. This is a direct result of the divisibility property...

bin packing is that the item sizes form a divisible sequence (also called factored). A special case of divisible item sizes occurs in memory allocation in...

divisors of n {\displaystyle n} becomes a partially ordered set if we use divisibility as the order relation. This partially ordered set is always a distributive...

is a list of notable integer sequences with links to their entries in the On-Line Encyclopedia of Integer Sequences. OEIS core sequences Index to OEIS...

The first 41 highly composite numbers are listed in the table below (sequence A002182 in the OEIS). The number of divisors is given in the column labeled...

37\%} . For a three-digit number that is divisible by 37, a rule of divisibility is that another divisible by 37 can be generated by transferring first...

properties of 1001 are the basis of a divisibility test for 7, 11 and 13. The method is along the same lines as the divisibility rule for 11 using the property...

"Sequence A111441 (Numbers k such that the sum of the squares of the first k primes is divisible by k)". The On-Line Encyclopedia of Integer Sequences...

{Z} [x,A,B]} . The division polynomials form a generic elliptic divisibility sequence over the ring Q [ x , y , A , B ] / ( y 2 − x 3 − A x − B ) {\displaystyle...