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10 votes
2 answers
380 views

Comparing two definite integrals analytically

10 votes
1 answer
356 views

$3\times 3$ matrices over $GF(3)$ which satisfy $A^{-1}=(A^T)^2$

9 votes
2 answers
280 views

How many nilpotent matrices are there in $M_n(\mathbb R)$ up to similarity?

7 votes
1 answer
396 views

Possible group operations on a finite set

6 votes
1 answer
191 views

Proof by contradiction using properties of normal subgroup: A group is cyclic if $x^m=e$ has at most $m$ solutions.

5 votes
1 answer
89 views

Expected rank of champion in a tournament where $P$(higher rank wins)$=\frac35$. Bracket is sorted by rank.

5 votes
2 answers
113 views

Suppose $f_1(x)=\sin(1+\sin(x))$, $f_2(x)=\sin(1+\sin(2+\sin(x)))$ and so on. Does $\lim_{n\to\infty}f_n(x)$ eventually become a constant function?

5 votes
3 answers
297 views

How to evaluate the definite integral $\int _{0}^{\frac{\pi }{2}}\frac{\ln(\tan x)}{1-\tan x+\tan^{2} x}\mathrm{d} x$?

5 votes
2 answers
206 views

Definite integral $ \int _{0}^{\infty } x\cdotp \tanh( 2x) \cdotp \ln(\coth x)\mathrm{d} x$

3 votes
1 answer
119 views

Using group theory, show that $\forall \ n\in \mathbb Z_{\geq 0}, \ (n+1)$ divides ${2n}\choose{n}$

3 votes
0 answers
74 views

Limit points of $\left\{\frac{1}{2^m}+\frac{1}{3^n}+\frac{1}{5^p}\ : \ m,n,p\in\mathbb N\right\}$

3 votes
3 answers
90 views

Show that the sequence $(3n-2)!!!/(3^n\cdot n!)$ converges to $0$.

3 votes
2 answers
255 views

Proving that Gauss-Jacobi iterations always converge when a system is strictly diagonally dominant.

3 votes
1 answer
219 views

Number of ways of placing $4$ knights on a $4 \times 4$ board such that for every knight, there is an unique knight attacking it

3 votes
1 answer
133 views

$n$- transposition permutations in $S_{2n}$ which decompose a $2n$-cycle into $n+1$ cycles

2 votes
1 answer
116 views

Binary sequences of $a$ zeros and $b$ ones which have $a+b$ circular shifts.

2 votes
2 answers
92 views

Bases of three $n$-dimensional subspaces of $\mathbb R^{2n}$ which have pairwise trivial intersection.

2 votes
1 answer
107 views

Values of $x_0$ for which the sequence defined by $x_{n+1}=\frac{(n^2+1)x_n^2}{x_n^3+n^2}$ is bounded.

2 votes
1 answer
174 views

Finding the solutions of $xp^2-2py+4x=0$

2 votes
2 answers
104 views

Expected length of sequence of positive integers which sums to $2023$

2 votes
1 answer
123 views

Given $m$ objects of type A and $n$ objects of type B, arrange them such that there are not more than two consecutive objects of type B.

2 votes
2 answers
140 views

How do you prove that $\sum\limits_{r=0}^{n}\binom{n}{r}\binom{n+r}{r} =\sum\limits_{r=0}^{n}( -1)^{n-r} 2^{r}\binom{n}{r}\binom{n+r}{r}$?

1 vote
1 answer
294 views

Alternate proof that $\cos(3A)+\cos(3B)+\cos(3C)=1-4\sin(\frac{3A}2)\sin(\frac{3B}2)\sin(\frac{3C}2)$ for $A$, $B$, $C$ the angles of a triangle

1 vote
1 answer
121 views

Definite Integral of $\int_{0}^{\pi /4}\tan x\cdotp \ln( 1+\sin 2x)\mathrm dx$ [closed]

1 vote
1 answer
56 views

Why the solution is wrong? $(x^2+x)\frac{d^2y}{ dx^2}+(2-x^2)\frac{ dy}{ dx}-(2+x)y=x(1+x)^2$

1 vote
0 answers
75 views

Additive Combinatorics: Dyson's transform

1 vote
2 answers
104 views

Showing that a recurrently defined sequence is convergent.

1 vote
2 answers
231 views

If all continuous functions $f:A\to \mathbb R$ are bounded, is the set $A$ necessarily compact?

1 vote
2 answers
159 views

Family of sets $\{A_i\}_{i=1}^n$ such that $A_i\not \subseteq A_j$ and $|A_i|\neq |A_j|$ for all distinct $i$,$j$.

1 vote
1 answer
107 views

Does similarity of matrices preserve sum of principal minors?