Newbetuts

$n \times n$ matrix whose entries $\in \{1,2\}$, such that $7$ divides the sum of every column and $5$ divides the sum of every row

Prove that $\forall p \in \Bbb P;p \ne 5,$ $F_{p^n - \left(\frac{5}{p}\right)p^{n-1}} \equiv 0 \mod p^n$

Show that $x^3 - 6x^2 + 11x - 6$ is divisible by $3, \forall x \in \mathbb{Z}$.

How many natural number between $100$ and $1000$ exist which can be expressed as sum of 10 different primes.

Chameleons of Three Colors puzzle

Nicer proof that $2^{n+2}$ divides $3^m-1$ if and only if $2^{n}$ divides $m$

Show that there exists a permutation satisfying a congruence equation.

Divisibility of $x^2+y^2$ by prime $p$ [duplicate]

Proof that $f(a)$ = $a$ div $d$ is onto

The cube of any number not a multiple of $7$, will equal one more or one less than a multiple of $7$

Find last three nonzero digits of $1^1 \cdot 2^2 \cdot 3^3 \cdot ... \cdot 25^{25}$

When is the map $x\rightarrow x^k$ injective in $\mathbb Z_n$?

How to calculate the power modulo $990$ without a calculator?

Prove by induction for $n\geq1, n \in \mathbb{N}$ $, 2^{2n+1}\equiv 9n^2-3n + 2\pmod{54}$.

Dividing the linear congruence equations

Prove $13^{17} \ne x^2 + y^5$

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Making the water gallon brainteaser rigorous

Finding the generators of a subgroup of $\mathrm{SL}_2(\mathbb Z)$

modulus in number theory

Primes for which $x^k\equiv n\pmod p$ is solvable: the fixed version

$n \times n$ matrix whose entries $\in \{1,2\}$, such that $7$ divides the sum of every column and $5$ divides the sum of every row

Prove that $\forall p \in \Bbb P;p \ne 5,$ $F_{p^n - \left(\frac{5}{p}\right)p^{n-1}} \equiv 0 \mod p^n$

Show that $x^3 - 6x^2 + 11x - 6$ is divisible by $3, \forall x \in \mathbb{Z}$.

How many natural number between $100$ and $1000$ exist which can be expressed as sum of 10 different primes.

Chameleons of Three Colors puzzle

Nicer proof that $2^{n+2}$ divides $3^m-1$ if and only if $2^{n}$ divides $m$

Show that there exists a permutation satisfying a congruence equation.

Divisibility of $x^2+y^2$ by prime $p$ [duplicate]

Proof that $f(a)$ = $a$ div $d$ is onto

The cube of any number not a multiple of $7$, will equal one more or one less than a multiple of $7$

Find last three nonzero digits of $1^1 \cdot 2^2 \cdot 3^3 \cdot ... \cdot 25^{25}$

When is the map $x\rightarrow x^k$ injective in $\mathbb Z_n$?

How to calculate the power modulo $990$ without a calculator?

Prove by induction for $n\geq1, n \in \mathbb{N}$ $, 2^{2n+1}\equiv 9n^2-3n + 2\pmod{54}$.

Dividing the linear congruence equations

Prove $13^{17} \ne x^2 + y^5$