User Elaqqad

24 votes

What is wrong with this putative proof?

answered Apr 2, 2015 at 20:56

17 votes

Accepted

Is this extension of Goldbach's conjecture obviously false?

answered Jul 9, 2015 at 11:18

17 votes

How to prove that the Fibonacci sequence is periodic mod 5 without using induction?

answered Jul 12, 2015 at 11:35

14 votes

Accepted

Can every even integer greater than four be written as a sum of two twin primes?

answered Mar 8, 2015 at 16:57

14 votes

Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.

answered Apr 11, 2015 at 16:35

12 votes

Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.

answered May 1, 2015 at 17:51

10 votes

If every element of G/H has finite order and every element of H has finite order, then every element of G has finite order

answered Apr 11, 2015 at 0:14

10 votes

Accepted

Integral of a square compared to the square of an integral

answered Apr 13, 2015 at 18:19

10 votes

When is a group isomorphic to a proper subgroup of itself?

answered Apr 14, 2015 at 1:21

10 votes

Accepted

Prove that $14322\mid n^{31} - n$

answered Apr 9, 2015 at 18:02

9 votes

Give an alternative proof of Wilson's theorem ($g$ is a primitive root modulo an odd prime $p$)

answered Apr 12, 2015 at 18:16

9 votes

Accepted

Index of a finite group

answered Apr 12, 2015 at 22:44

9 votes

Factor $k^{4}+4k^{3}+8k^{2}+8k+4=0$ over $\mathbb C$

answered Aug 6, 2015 at 18:49

8 votes

Accepted

Proof that $(n^7-n^3)(n^5+n^3)+n^{21}-n^{13}$ is a multiple of $3$.

answered May 1, 2015 at 19:04

8 votes

Accepted

Infiniteness of the set of primes such $f$ have root $\bmod p$

answered Apr 24, 2015 at 19:19

8 votes

$p$-series divided by alternating $p$-series = geometric series? Why?

answered Apr 27, 2015 at 16:00

8 votes

Show the series $e^{-\cos n}$ diverges.

answered Apr 14, 2015 at 1:02

8 votes

Accepted

Find the sum of all odd numbers between two polynomials

answered Apr 8, 2015 at 23:33

8 votes

Show that if $n$ is composite, then $\phi(n) \leq n-\sqrt{n}$

answered Mar 6, 2015 at 18:12

8 votes

Accepted

$P(z)=0$ iff $Q(z)=0$, $P(z)=1$ iff $Q(z)=1$. Prove that $P(x)=Q(x)$ for all $x$

answered Jan 26, 2015 at 12:15

7 votes

Accepted

Prove $\limsup_{n\to\infty}|\{(p,q)\in T\times T,p!q!=n\}|=6$

answered Feb 9, 2015 at 16:02

7 votes

Accepted

$n(n+1)(n+2)$ is not a perfect power

answered Mar 4, 2015 at 22:48

7 votes

Accepted

What is the mistake in this proof?

answered Apr 9, 2015 at 15:55

7 votes

Cyclic group Zp

answered Apr 18, 2015 at 13:32

7 votes

Accepted

Show that if $x,y,z$ are positive integers, then $(xy + 1)(yz + 1)(zx + 1)$ is a perfect square iff $xy +1, yz +1, zx+1$ are all perfect squares.

answered Mar 19, 2016 at 14:20

6 votes

Prove that for any real number the inequality is true: $x^4-x^3+5x^2 > 3x - 6$

answered Apr 18, 2015 at 23:56

6 votes

Accepted

Find all prime numbers $p$ such that $p \mid 2^p + 1$

answered Apr 18, 2015 at 22:14

6 votes

What is the limit as k approaches infinity of $(k!)^{\frac{1}{k}}$

answered Apr 10, 2015 at 20:25

6 votes

Accepted

Proving $(1+\frac 1n)^{n} = 1 + \sum_{k=1}^n({\frac 1{k!}\prod_{r=0}^{k-1}(1-\frac rn))}$ using the binomial theorem

answered Apr 6, 2015 at 14:35

6 votes

Accepted

For each irrational number $b$, does there exist an irrational number $a$ such that $a^b$ is rational?

answered Apr 7, 2015 at 15:33

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404 Answers

What is wrong with this putative proof?

Is this extension of Goldbach's conjecture obviously false?

How to prove that the Fibonacci sequence is periodic mod 5 without using induction?

Can every even integer greater than four be written as a sum of two twin primes?

Elementary proof for $\sqrt{p_{n+1}} \notin \mathbb{Q}(\sqrt{p_1}, \sqrt{p_2}, \ldots, \sqrt{p_n})$ where $p_i$ are different prime numbers.

Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.

If every element of G/H has finite order and every element of H has finite order, then every element of G has finite order

Integral of a square compared to the square of an integral

When is a group isomorphic to a proper subgroup of itself?

Prove that $14322\mid n^{31} - n$

Give an alternative proof of Wilson's theorem ($g$ is a primitive root modulo an odd prime $p$)

Index of a finite group

Factor $k^{4}+4k^{3}+8k^{2}+8k+4=0$ over $\mathbb C$

Proof that $(n^7-n^3)(n^5+n^3)+n^{21}-n^{13}$ is a multiple of $3$.

Infiniteness of the set of primes such $f$ have root $\bmod p$

$p$-series divided by alternating $p$-series = geometric series? Why?

Show the series $e^{-\cos n}$ diverges.

Find the sum of all odd numbers between two polynomials

Show that if $n$ is composite, then $\phi(n) \leq n-\sqrt{n}$

$P(z)=0$ iff $Q(z)=0$, $P(z)=1$ iff $Q(z)=1$. Prove that $P(x)=Q(x)$ for all $x$

Prove $\limsup_{n\to\infty}|\{(p,q)\in T\times T,p!q!=n\}|=6$

$n(n+1)(n+2)$ is not a perfect power

What is the mistake in this proof?

Cyclic group Zp

Show that if $x,y,z$ are positive integers, then $(xy + 1)(yz + 1)(zx + 1)$ is a perfect square iff $xy +1, yz +1, zx+1$ are all perfect squares.

Prove that for any real number the inequality is true: $x^4-x^3+5x^2 > 3x - 6$

Find all prime numbers $p$ such that $p \mid 2^p + 1$

What is the limit as k approaches infinity of $(k!)^{\frac{1}{k}}$

Proving $(1+\frac 1n)^{n} = 1 + \sum_{k=1}^n({\frac 1{k!}\prod_{r=0}^{k-1}(1-\frac rn))}$ using the binomial theorem

For each irrational number $b$, does there exist an irrational number $a$ such that $a^b$ is rational?