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PNT's user avatar
PNT's user avatar
PNT
  • Member for 3 years, 1 month
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5 votes
Accepted

A sequence is defined by the nth term: $n^3 -21n^2 +99n +121$. What primes does the sequence contain if continued to infinity?

5 votes

Set of primes dividing $2^n+3^n$.

5 votes

Placing an integer's divisors around a circle

4 votes

Given $x^4+y^4+z^4=1$ Find the minimum value of $\sum_{cyc}\frac{x^3}{1-x^8}$.

3 votes

Proving by induction that $\frac{1}{n} \ge \frac{n!}{n^n}$

3 votes

Inscribed angle theorem using complex numbers.

2 votes

proving that $ab$ is a perfect square.

2 votes

Prove: if $n\mid 7^n+6^n$ and $n>1$, then $13\mid n$

2 votes
Accepted

A formula which equals $1$ at $x=0$ and $0$ otherwise

2 votes
Accepted

Find all positive integers $n$ s.t. $3n-2\mid n^{3n-2}-3n+1$

2 votes
Accepted

Integration of a function not defined at a point

2 votes
Accepted

Determine $\frac{\partial f(x, y, z)}{\partial x}$ where $z$ is a function $z(x), z:\mathbb{R}_+\mapsto \mathbb{R}_+$?

1 vote
Accepted

Find a linear transformation $T\begin{pmatrix}-1\\-2\end{pmatrix}$

1 vote

Prove convergence of $\int_0^1 \frac{\ln(x)}{1-x^2} dx$

1 vote

Prove that $3^{2n} +7$ is divisible by 8

1 vote

Proving that $\gcd\left(\frac a {\gcd(a,b)},\frac b {\gcd(a,b)}\right) =1$

1 vote

Find all $n \in \mathbb{N}$ such that $(n+2) \mid (n^2+5)$

1 vote

Antiderivative of a polynomial fraction

1 vote

Prove $|\int_{a}^{b}f(x)dx| \le \int_{a}^{b}|f(x)|dx $

1 vote

Prove that $\angle AED = 2 \cdot \angle BEC$

1 vote

Prove that $a^ n\equiv b^n\pmod{p^k}$ if and only if $n(a-b)\equiv 0 \pmod{p^k}$

1 vote
Accepted

Let $a_{n+3}=a_{n+2}+a_{n+1}+a_n$ Prove that $\forall N\in \mathbb Z^+ , \exists a_k$ s.t. $N\mid a_k$

1 vote

How to find the number of ordered pairs $(A,B)$, where $A$ and $B$ are subsets of $S$ and $A$ is a proper subset of $B$.

0 votes

Showing $\sum_{i=1}^n\frac{x_i}{x_{i+1}}+\frac{2^{n+1}}{\prod\left(1+\frac{x_i}{x_{i+1}}\right)}\ge n+2$, for $n\geq2$ and for positive real $x_i$

0 votes

Count how many $(a_1,...,a_n)$ such that $a_1+...+a_n\ge n^2$ and $a_1^2+...+a_n^2\le n^3+1$.

0 votes

For any odd prime $p \gt 1$, show that $2^p \equiv 8 \pmod {12}$

0 votes

On the GCD of a Pair of Fermat Numbers

0 votes

If $n \mid a^n - 1$, prove $ a + 1 $, $ a^2 + 2 $, ..., $ a^n + n $ are distinct $ \bmod n $.

0 votes

Inequality $a^2+2b^2+8c^2\geq2a(b+2c)$

0 votes

Prove that $6|n(n+1)(2n+1)$, $n\in\mathbb{Z}$