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Elaqqad
  • Member for 7 years, 7 months
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23 votes

What is wrong with this putative proof?

17 votes

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

16 votes
Accepted

Is this extension of Goldbach's conjecture obviously false?

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.

14 votes
Accepted

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

12 votes

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

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

10 votes
Accepted

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

10 votes
Accepted

Integral of a square compared to the square of an integral

9 votes
Accepted

Index of a finite group

9 votes

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

8 votes
Accepted

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

8 votes

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

8 votes

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

8 votes

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

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 $x$

7 votes

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

7 votes
Accepted

What is the mistake in this proof?

7 votes
Accepted

Find the sum of all odd numbers between two polynomials

7 votes
Accepted

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

7 votes
Accepted

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

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.

6 votes

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

6 votes

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

6 votes

Cyclic group Zp

6 votes
Accepted

Infiniteness of set of primes such $f$ have root $\mod p$

6 votes

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

6 votes
Accepted

Estimation of a combinatorial sum

6 votes

Simplifying $\sum_{k=0}^{\lfloor{\frac{n}{2}}\rfloor}\binom{n}{2k}2^{2k}$

6 votes
Accepted

When is a rational number a sum of three squares?

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