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New posts in divisibility
Divisibility criteria for $7,11,13,17,19$
elementary-number-theory
divisibility
If $a \mid m$ and $(a + 1) \mid m$, prove $a(a + 1) | m$.
number-theory
divisibility
gcd-and-lcm
least-common-multiple
For any prime $p > 3$, why is $p^2-1$ always divisible by 24?
elementary-number-theory
prime-numbers
divisibility
Compute polynomial $p(x)$ if $x^5=1,\, x\neq 1$ [reducing mod $\textit{simpler}$ multiples]
polynomials
ring-theory
modular-arithmetic
proof-explanation
divisibility
The product of $n$ consecutive integers is divisible by $n$ factorial
elementary-number-theory
divisibility
factorial
$\gcd(a,b,c)=\gcd(\gcd(a,b),c)\,$ [Associative Law for GCD, LCM]
elementary-number-theory
divisibility
gcd-and-lcm
Why $9$ & $11$ are special in divisibility tests using decimal digit sums? (casting out nines & elevens)
elementary-number-theory
modular-arithmetic
divisibility
decimal-expansion
Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]
elementary-number-theory
divisibility
gcd-and-lcm
Why is $a^n - b^n$ divisible by $a-b$?
elementary-number-theory
modular-arithmetic
induction
divisibility
congruences
Why $\gcd(b,qb+r)=\gcd(b,r),\,$ so $\,\gcd(b,a) = \gcd(b,a\bmod b)$
abstract-algebra
elementary-number-theory
divisibility
gcd-and-lcm
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
elementary-number-theory
induction
divisibility
gcd-and-lcm
Divisibility by 7 rule, and Congruence Arithmetic Laws
elementary-number-theory
divisibility
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