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• https://en.wikipedia.org/wiki/Divisibility_rule — found via Wikipedia

  Divisibility rule

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

  Divisibility sequence sequences with values in any ring where the concept of divisibility is defined. A strong divisibility sequence is an integer sequence ( a n ) {\displaystyle
  Divisor definition, to elements of any ring; see Divisibility (ring theory). An integer n {\displaystyle n} is divisible by a nonzero integer m {\displaystyle m}
  Infinite divisibility Infinite divisibility arises in different ways in philosophy, physics, economics, order theory (a branch of mathematics), and probability theory (also

• https://projecteuler.net/problem=601 — found via Mwmbl

  #601 Divisibility Streaks - Project Euler

  Divisibility Streaks Problem 601 For every positive number $n$ we define the function $\mathop{streak}(n)=k$ as the smallest positive integer $k$ such th…

  #549 Divisibility of Factorials - Project Euler

• http://pastebin.com/Dkbq2chV — found via Mwmbl

  Better divisibility rule finder - Pastebin.com

• http://arxiv.org/abs/1801.02260 — found via Mwmbl

  [1801.02260] Divisibility classes are seldom closed under flat c…

  Title:Divisibility classes are seldom closed under flat covers Abstract:It is well-known that a class of all modules, which are torsion-free with respect…

  [1511.01731] Divisibility orders in $βN$ Title:Divisibility orders in $βN$ Abstract:We consider five divisibility orders on the Stone-Čech compactification $\beta N$. We find antichains of incom…
  [0903.4346] Divisibility of characteristic numbers Title:Divisibility of characteristic numbers Abstract: We use homotopy theory to define certain rational coefficients characteristic numbers with integra…
  [1212.6221] Divisibility properties of the Fibonacci entry point Title:Divisibility properties of the Fibonacci entry point Abstract:For a prime $p$, let $Z(p)$ be the smallest positive integer $n$ so that $p$ divides …
  [1407.7923] Divisibility of Weil Sums of Binomials Title:Divisibility of Weil Sums of Binomials Abstract:Consider the Weil sum $W_{F,d}(u)=\sum_{x \in F} \psi(x^d+u x)$, where $F$ is a finite field of cha…
  [1609.04750] Divisibility sequences of polynomials and heights e… Title:Divisibility sequences of polynomials and heights estimates Abstract:In this note we compute a constant $N$ that bounds the number of non--primitiv…
  [math/0701247] Divisibility of the stable Miller-Morita-Mumford … Title:Divisibility of the stable Miller-Morita-Mumford classes Abstract: We determine the sublattice generated by the Miller-Morita-Mumford classes $\kap…
  [2302.02243] Divisibility Properties of Integer Sequences Title:Divisibility Properties of Integer Sequences Abstract:A sequence of nonzero integers $f = (f_1, f_2, \dots)$ is ``binomid'' if every $f$-binomid co…
  [0807.2629] Divisibility by 2 and 3 of certain Stirling numbers Title:Divisibility by 2 and 3 of certain Stirling numbers Abstract: The numbers e_p(k,n) defined as min(nu_p(S(k,j)j!): j >= n) appear frequently in alge…
  [1010.2275] Divisibility of Power Sums and the Generalized Erdos… Title:Divisibility of Power Sums and the Generalized Erdos-Moser Equation Abstract:Using elementary methods, we determine the highest power of 2 dividing…
  [1311.1366] Divisibility of Trinomials by Irreducible Polynomial… Title:Divisibility of Trinomials by Irreducible Polynomials over F2 Abstract:Irreducible trinomials of given degree n over $F_2$ do not always exist and …
  [2004.05255] Divisibility Results for zero-cycles Title:Divisibility Results for zero-cycles Abstract:Let $X$ be a product of smooth projective curves over a finite unramified extension $k$ of $\mathbb{Q…
  [1710.10884] Divisibility of binomial coefficients by powers of … Title:Divisibility of binomial coefficients by powers of two Abstract:For nonnegative integers $j$ and $n$ let $\Theta(j,n)$ be the number of entries in …
  [2405.05274] Divisibility of an analogue of $t$-core partition f… Title:Divisibility of an analogue of $t$-core partition function by powers of primes Abstract:A partition of a positive integer $n$ is said to be $t$-cor…
  [1903.04903] Divisibility Tests Unified: Stacking the Trimmings … Title:Divisibility Tests Unified: Stacking the Trimmings for Sums Abstract:Divisibility tests are algorithms that can quickly decide if one integer is di…
  [2008.13475] Divisibility and Arithmetic Properties of a Class o… Title:Divisibility and Arithmetic Properties of a Class of Sparse Polynomials Abstract:We investigate algebraic and arithmetic properties of a class of s…
  [1511.01731v2] Divisibility orders in $βN$ Title:Divisibility orders in $βN$ Abstract:We consider five divisibility orders on the Stone-Čech compactification $\beta N$. We find antichains of incom…
  [1010.2275v3] Divisibility of Power Sums and the Generalized Erd… Title:Divisibility of Power Sums and the Generalized Erdos-Moser Equation Abstract:Using elementary methods, we determine the highest power of 2 dividing…
  [1311.1366v2] Divisibility of Trinomials by Irreducible Polynomi… Title:Divisibility of Trinomials by Irreducible Polynomials over F2 Abstract:Irreducible trinomials of given degree n over $F_2$ do not always exist and …
  [1010.2275v4] Divisibility of Power Sums and the Generalized Erd… Title:Divisibility of Power Sums and the Generalized Erdos-Moser Equation Abstract:Using elementary methods, we determine the highest power of 2 dividing…
  [1407.7923v1] Divisibility of Weil Sums of Binomials Title:Divisibility of Weil Sums of Binomials Abstract:Consider the Weil sum $W_{F,d}(u)=\sum_{x \in F} \psi(x^d+u x)$, where $F$ is a finite field of cha…
  [1407.7923v3] Divisibility of Weil Sums of Binomials Title:Divisibility of Weil Sums of Binomials Abstract:Consider the Weil sum $W_{F,d}(u)=\sum_{x \in F} \psi(x^d+u x)$, where $F$ is a finite field of cha…
  [1406.0402] On Divisibility Properties of Truncated Binomial Ser… Title:On Divisibility Properties of Truncated Binomial Series Abstract:The divisibility of truncated binomial series by their exponent n is analyzed. Div…
  [1407.7923v2] Divisibility of Weil Sums of Binomials Title:Divisibility of Weil Sums of Binomials Abstract:Consider the Weil sum $W_{F,d}(u)=\sum_{x \in F} \psi(x^d+u x)$, where $F$ is a finite field of cha…
  [2311.05369] Divisibility properties of polynomial expressions o… Abstract:We study divisibility properties of a set $\{f_1(\mathbf{U}_n^{(s)}),\ldots,f_m(\mathbf{U}_n^{(s)})\}$, where $f_1,\ldots,f_m$ are polynomials i…

• http://math.stackexchange.com/a/398353 — found via Mwmbl

  divisibility - System of two simple modular equations - Mathemat…

  I need to find the smallest x for which these equations can be solved. I've been always doing this using Chinese Reminder Theorem, but it seems that it do…

  divisibility - Is $x/x$ equal to $1$ - Mathematics Stack Exchange $\begingroup$What is the value of $\frac{2x}{x}$ everywhere except 0? What "should" the value then be? The limit gives you exactly this. The value you "s…
  divisibility - Division of $q^n-1$ by $q^m-1$, in Wedderburn's t… $\begingroup$The argument with the roots of unity show that, as a polynomial, if $q^m-1\;|\;q^n-1$, then $m\;|\;n$. I don't see how it shows that there m…
  divisibility - How come the number $N!$ can terminate in exactly… $\begingroup$@Aryabhata I followed Bill's suggestion in the comments to my answer. I have hence created a new question with the answer. Bill "The problem…