Newbetuts

Showing that gcd does not exist for $3(1+\sqrt{-5})$ and $3(1-\sqrt{-5})$ in $\mathbb Z[\sqrt{-5}]$.

Why does every number of shape ababab is divisible by $13$?

$3$ never divides $n^2+1$

Proof of the divisibility rule of 17.

Factor of a Mersenne number [duplicate]

Is 1100 a valid state for this machine?

How to prove that $k^3+3k^2+2k$ is always divisible by $3$? [closed]

My first proof that uses the well-ordering principle (very simple number theory). Please mark/grade.

Numbers from $1$ to $n$ are permuted such that the sum of any three consecutive numbers is divisible by the leftmost of them

Considering the set of integers between 77-999, inclusive, how many are divisible by no less than three of the numbers 2, 3, 6 and 8?

If $2^{2k}-x^2\bigm|2^{2k}-1$ then $x=1$ [duplicate]

Why this algorithm for egyptian fractions doesn't terminate in ~$2$% cases?

Suppose $a$ and $b$ are relatively prime and $x \in \mathbb{Z}$. Show that if $a|bx$, them $a|x$ [duplicate]

Prove $\,a\mid bc\!\!\iff\!\! a\mid(a,b)c\!\iff\!\!\frac{a}{(a,b)}\!\mid c\ $ [general Euclid's Lemma]

Find all positive integers $(a,b)$ such that $\displaystyle\frac{a^{2^{b}}+b^{2^{a}}+11}{2^{a}+2^{b}}$ is an integer

What is complete induction, by example? $4(9^n) + 3(2^n)$ is divisible by 7 for all $n>0$

Integers $x$ such that $\frac{nx}{x-n}$ is an integer

New posts in divisibility

Proof for divisibility by $7$

Divisibility of $2^n - 1$ by $2^{m+n} - 3^m$.

A solution using 'Lifting the exponent' lemma to IMO 1990 P3

Showing that gcd does not exist for $3(1+\sqrt{-5})$ and $3(1-\sqrt{-5})$ in $\mathbb Z[\sqrt{-5}]$.

Why does every number of shape ababab is divisible by $13$?

$3$ never divides $n^2+1$

Proof of the divisibility rule of 17.

Factor of a Mersenne number [duplicate]

Is 1100 a valid state for this machine?

How to prove that $k^3+3k^2+2k$ is always divisible by $3$? [closed]

My first proof that uses the well-ordering principle (very simple number theory). Please mark/grade.

Numbers from $1$ to $n$ are permuted such that the sum of any three consecutive numbers is divisible by the leftmost of them

Considering the set of integers between 77-999, inclusive, how many are divisible by no less than three of the numbers 2, 3, 6 and 8?

If $2^{2k}-x^2\bigm|2^{2k}-1$ then $x=1$ [duplicate]

Why this algorithm for egyptian fractions doesn't terminate in ~$2$% cases?

Suppose $a$ and $b$ are relatively prime and $x \in \mathbb{Z}$. Show that if $a|bx$, them $a|x$ [duplicate]

Prove $\,a\mid bc\!\!\iff\!\! a\mid(a,b)c\!\iff\!\!\frac{a}{(a,b)}\!\mid c\ $ [general Euclid's Lemma]

Find all positive integers $(a,b)$ such that $\displaystyle\frac{a^{2^{b}}+b^{2^{a}}+11}{2^{a}+2^{b}}$ is an integer

What is complete induction, by example? $4(9^n) + 3(2^n)$ is divisible by 7 for all $n>0$

Integers $x$ such that $\frac{nx}{x-n}$ is an integer