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ulead86
  • Member for 11 years
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13 votes
1 answer
519 views

Chebyshev: Proof $\prod \limits_{p \leq 2k}{\;} p > 2^k$

8 votes
1 answer
4k views

Sufficient / necessary conditions for $g \circ f$ being injective, surjective or bijective

8 votes
1 answer
648 views

Proof: $\phi(n)=\sum\limits_{k=1}^{n-1} \left\lfloor\frac{1}{\operatorname{gcd}(n,k)} \right\rfloor$

8 votes
1 answer
814 views

Proof: If $n \in \mathbb{N}$ is not the sum of two squares, then $n$ is also not the sum of two rational squares

6 votes
1 answer
2k views

Cramer's rule: Geometric Interpretation

5 votes
3 answers
264 views

Solving congruences

5 votes
4 answers
1k views

Bell Numbers: How to put EGF $e^{e^x-1}$ into a series?

5 votes
1 answer
175 views

Dice game modelling: Lose everything on "3", double everything on "1" or "6"

5 votes
5 answers
310 views

Proof: $\vec x,\vec y \perp \vec z \Rightarrow \vec x || \vec y$

4 votes
2 answers
1k views

Counterexample for $R(4,4) \neq 8$

4 votes
2 answers
160 views

$x,y$ are linearly depending iff $|\langle x,y\rangle|=\|x\| \cdot \|y\|$

4 votes
4 answers
210 views

Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$

4 votes
3 answers
2k views

Continued fraction: Show $\sqrt{n^2+2n}=[n; \overline{1,2n}]$

4 votes
3 answers
798 views

Show that every power of $2$ is sum of two squares.

3 votes
2 answers
80 views

Why doesn't work Integer factorization for fields?

3 votes
2 answers
780 views

Reciprocal of a continued fraction

3 votes
3 answers
252 views

Proofs from the BOOK: Bertrand's postulate: $\binom{2m+1}{m}\leq 2^{2m}$

3 votes
1 answer
761 views

How to prove $\sum_{ d \mid n} \mu(d)f(d)=\prod_{i=1}^r (1-f(p_i))$?

3 votes
1 answer
1k views

Proof: $S(n)=2^{\omega(n)}$ where $S(n)$ is the number of squarefree divisors of n

3 votes
2 answers
365 views

Proofs from the BOOK: Bertrand's postulate Part 3: $\frac{2}{3}n<p \leq n \rightarrow$ no p divides $\binom{2n}{n}$

3 votes
2 answers
2k views

maximum area of semi-circle in square

3 votes
1 answer
54 views

Find $ \vec{z} \parallel \vec{x}$ and $\vec{y}-\vec{z} \perp \vec{x}$

2 votes
1 answer
3k views

Two Circles intersecting, common tangent: Proof $GI=IH$

2 votes
2 answers
83 views

Prove an inequality in $\mathbb{R}$

2 votes
1 answer
57 views

limit of sequences $c_n=(-2)^n$ and $d_n=\frac{n^3+1}{n^2}$

2 votes
1 answer
344 views

Proofs from the BOOK: Bertrand's postulate: proof $\lfloor \frac{2n}{p^k} \rfloor - 2 \lfloor \frac{n}{p^k} \rfloor= 2$

2 votes
1 answer
2k views

Prove that $e^{\sqrt{\log x }}=O(x^n)$

2 votes
1 answer
123 views

Show $p(n)=n(p_{n-1}+p_{n-2})+(n-1)p_{n-3}+(n-2)p_{n-4}+...+3p_1+2p_0+2$

2 votes
1 answer
112 views

Proof $\left|N\right|=\left|M\right|$ with $M=(n_1,...n_s) \mid n_i$ and $N=(n_1,...,{n_s+1}) \mid n_i$

2 votes
1 answer
85 views

How to get "N" from $k=\log_2(N)$