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New posts in divisibility
Divisibility is transitive: $\ a\mid b\mid c\,\Rightarrow\ a\mid c$
arithmetic
divisibility
Prime divisors of $k^2+(k+1)^2$
number-theory
elementary-number-theory
prime-numbers
algebraic-number-theory
divisibility
How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction? [duplicate]
elementary-number-theory
induction
divisibility
Prove that $6$ divides $n(n + 1)(n + 2)$
elementary-number-theory
divisibility
What is vector division?
calculus
vectors
divisibility
Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$? [duplicate]
number-theory
elementary-number-theory
contest-math
divisibility
Proof of Wolstenholme's theorem
number-theory
elementary-number-theory
prime-numbers
proof-writing
divisibility
Prove that there exist infinitely many integers $(n^{2015}+1)\mid n!$
number-theory
divisibility
factorial
conjectures
$ac\equiv bc \pmod{\!m}\!\!\iff\!\! a\equiv b \pmod{\!\!\frac{m}{(c,m)}}$ [Euclid's Lemma, congruence form]
elementary-number-theory
modular-arithmetic
divisibility
Proving by strong induction that $\forall n \ge 2, \;\forall d \ge 2 : d \mid n(n+1)(n+2)...(n+d-1) $
elementary-number-theory
proof-writing
induction
divisibility
cancelling out before evaluation of variable
abstract-algebra
polynomials
divisibility
Prove that $(a-b) \mid (a^n-b^n)$ [duplicate]
elementary-number-theory
proof-writing
induction
divisibility
8...8d5...5 is divisible by 11
elementary-number-theory
prime-numbers
divisibility
If a prime number is reversed, and then appended to itself, why is the result always a composite number?
elementary-number-theory
prime-numbers
divisibility
pattern-recognition
Is sum of digits of $3^{1000}$ divisible by $7$?
elementary-number-theory
modular-arithmetic
arithmetic
divisibility
decimal-expansion
$ d = \gcd(a,b)\Rightarrow\ \gcd(a/d,b/d) = 1$
elementary-number-theory
divisibility
Show $a\Bbb Z+b\Bbb Z = \gcd(a,b)\Bbb Z$
elementary-number-theory
proof-writing
divisibility
Is $f(a)\!=\!0\!=\!f(b)\Rightarrow (x\!-\!a)(x\!-\!b)\mid f(x)\,$ true if $\,a=b?\ $ [Double Factor Theorem]
polynomials
divisibility
factoring
How to prove that all odd powers of two add one are multiples of three
elementary-number-theory
arithmetic
divisibility
Find all positive integers $n$ s.t. $3^n + 5^n$ is divisible by $n^2 - 1$
number-theory
divisibility
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