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...

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

Lehmer sequences are examples of divisibility sequences. It is also known that if ( W n ) n ≥ 1 {\displaystyle (W_{n})_{n\geq 1}} is an elliptic divisibility...

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

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

2y\mathbb {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 )...

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

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...

In mathematics, elliptic curve primality testing techniques, or elliptic curve primality proving (ECPP), are among the quickest and most widely used methods...

computer science have been brought to bear on this problem, including elliptic curves, algebraic number theory, and quantum computing. Not all numbers...

Eisenstein's criterion, a test for whether a polynomial is irreducible based on divisibility of its coefficients by a prime number and its square. The concept of...

a nonzero perfect square divisible by 16. Primitive Pythagorean triples have been used in cryptography as random sequences and for the generation of...

proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential operator on a compact manifold, the analytical index (related...

77232917, 82589933, 136279841. (sequence A000043 in the OEIS) Since they are prime numbers, Mersenne primes are divisible only by 1 and themselves. However...

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...

40, ... (sequence A005835 in the OEIS) Every multiple of a semiperfect number is semiperfect. A semiperfect number that is not divisible by any smaller...

134, 135, 136, 138, 140, 141, 142, 143, 144, 145, 146, 147, 148, 150. (sequence A002808 in the OEIS) Every composite number can be written as the product...

original on 2022-09-25. Retrieved 2020-09-07. Lee, Elvin (1969). "On Divisibility by Nine of the Sums of Even Amicable Pairs". Mathematics of Computation...

4294967297, 18446744073709551617, 340282366920938463463374607431768211457, ... (sequence A000215 in the OEIS). If 2k + 1 is prime and k > 0, then k itself must...

= 7, and W512 = M521. Like Cullen numbers, Woodall numbers have many divisibility properties. For example, if p is a prime number, then p divides W(p + 1) / 2...

used for quick divisibility tests: a natural number is divisible by 3 or 9 if and only if its digit sum (or digital root) is divisible by 3 or 9, respectively...

number of divisors whose sum is also perfect. There are twelve Jacobian elliptic functions and twelve cubic distance-transitive graphs. A twelve-sided polygon...

n Z < Z ≅ π1 (PSL(2, R)), which form a lattice of covering groups by divisibility; these cover SL(2, R) if and only if n is even. The center of SL(2, R)...

often used in the context of elliptic curves. Let E / K {\displaystyle E/K} be an elliptic curve. There is a short exact sequence 0 → E [ m ] → E → P ↦ m ⋅...

its sequence of partial sums. Either the sequence of partial sums or the sequence of terms completely characterizes the series, and the sequence of terms...

P(n) divisible by composite index n was found only in 1982 by William Adams and Daniel Shanks. They presented a detailed investigation of the sequence, with...

using trial division to sequentially test each candidate number for divisibility by each prime. Once all the multiples of each discovered prime have been...

remainder upon division by 9 will be 0), which allows it to be used as a divisibility rule. Let n {\displaystyle n} be a natural number. For base b > 1 {\displaystyle...

3200, 3267, 3456, 3528, 3872, 3888, 4000, 4232, 4500, 4563, 4608, 5000 (sequence A052486 in the OEIS). The smallest pair of consecutive Achilles numbers...