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KON3's user avatar
KON3's user avatar
KON3
  • Member for 11 years, 6 months
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20 votes

Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer

9 votes
Accepted

Sum $\sum_{n=2}^{\infty} \frac{n^4+3n^2+10n+10}{2^n(n^4+4)}$

8 votes

Evaluate $\int\frac{\cos^2 x}{1-\sin x }dx$

7 votes
Accepted

what is remainder when $(((3!)^{5!})^{7!})^{9!...}$ is divided by 11

6 votes

How to get from $\frac{n(n+1)}{2}$ to $n + \binom{n}{2}$?

5 votes

Is $x^4+x+1$ irreducible in $\Bbb{Q}[x]$?

3 votes

Prove or disprove $\sum (a_n + b_n) $ is divergent if $\sum a_n $ and $\sum b_n $ are divergent.

3 votes

If $ \operatorname{Tr}(M^k) = \operatorname{Tr}(N^k)\;\forall 1\leq k \leq n$, then how do we show the $M$ and $N$ have the same eigenvalues?

3 votes

Calculate sum of an infinite series

3 votes

$d\mid n\Longrightarrow d\leq\sqrt n$

3 votes
Accepted

Prove that $(A^c \cup B^c) - A = A^c $

3 votes
Accepted

How do I solve $\sum_{n=5}^\infty \frac{12}{16 \, n^{2} + 40 \, n + 21}$

3 votes
Accepted

find coefficient of $x^{50}$

3 votes
Accepted

Evaluate $\int 7\tan^5x\sec^2 x\,dx$

2 votes

Show that the permutation $(1 \space 2 \space 3)$ can not be a cube of any element of $S_n.$

2 votes

Find the units and zero divisors of $\mathbb Z_3 \oplus\mathbb Z_{6}$

1 vote

How would I show that R is an equivalence relation?

1 vote

Whole number and rational number relationship

1 vote

Prove the sum to n terms of the series

1 vote

When to use the $\equiv$ symbol (such as in $5^{6}$ $\equiv$ 1 mod 7) vs =

1 vote

How many elements in $X$ are of the form $3k + 1$ for some integer $k$?

1 vote

Calculate the 50th power of a matrix

1 vote

How to show the Symmetric Group $S_4$ has no elements of order $6$.

1 vote

solving $\int x^7\sqrt{3+2x^4}dx$

1 vote

Prob. 7, Chap. 3 in Baby Rudin: If $a_n \geq 0$, then how does convergence of $\sum a_n$ imply convergence of $\sum \frac{\sqrt{a_n}}{n}$?

1 vote

If $n$ be a proper divisor of $a=|C_a|$ then what should be closed form of $\sum\limits_{d|n}\eta_d(C_a)$?

1 vote
Accepted

Sum $S=a_1+a_2+...+a_{2015}$

0 votes

How shall we show that the only possible orders of any element in dihedral group $D_n$ will be either a divisor of 2 or $n$?

0 votes
Accepted

How do I show that $b^8=a^3ba^{-3}$?

0 votes

Find the order of $(3,1)+\langle0,2\rangle$ in $ \Bbb Z_{4}\oplus \Bbb Z_{8}/\langle0,2\rangle$