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21 votes

2 answers

3k views

Calculate $\int_{0}^{1} (x-f(x))^{2016} dx$, given $f(f(x))=x$.

definite-integrals

asked May 8, 2016 at 14:13

15 votes

1 answer

9k views

domain of $x^x$

exponential-function

asked Nov 29, 2015 at 14:33

9 votes

1 answer

158 views

Cyclic system of cubic equations in $5$ variables

algebra-precalculus

asked Jun 2, 2016 at 17:20

8 votes

1 answer

177 views

Given $a+b+..=a^7+b^7+..=0$ show that $a(a+b)..=0$ [duplicate]

algebra-precalculus contest-math

asked Apr 21, 2016 at 17:47

8 votes

2 answers

976 views

Why was it necessary for the Riemann integral to consider all partitions and taggings?

real-analysis soft-question riemann-integration

asked Jan 6, 2017 at 17:49

7 votes

1 answer

606 views

One of the diagonals in a hexagon cuts of a triangle of area $\leq 1/6^{th}$ of the hexagon

geometry

asked May 19, 2016 at 6:32

5 votes

5 answers

239 views

For integer $n>2$, $(n!)^2 > n^n$ [duplicate]

inequality exponentiation factorial

asked May 4, 2016 at 17:14

4 votes

0 answers

29 views

Inequality involving integration [duplicate]

integration inequality

asked Dec 29, 2015 at 9:06

4 votes

3 answers

322 views

Partitioning of sets

number-theory set-partition

asked Jan 3, 2016 at 14:34

3 votes

2 answers

356 views

$2^{49}$ ways to choose a set of integers $\leq 50$ with odd sum

combinatorics

asked May 5, 2016 at 15:48

3 votes

4 answers

227 views

Show that $\{a_n\}$ defined by $a_{n+1}=\frac{a_n+2}{a_n+1}$ converges

sequences-and-series convergence-divergence

asked Jun 9, 2016 at 19:07

3 votes

3 answers

763 views

Number of labelled trees on $n$ vertices containing $2$ fixed non-adjacent edges

combinatorics graph-theory trees

asked Mar 14, 2018 at 19:04

3 votes

1 answer

158 views

Automorphism group of finite $k$-algebra as an affine variety

algebraic-geometry commutative-algebra

asked Sep 19, 2020 at 15:57

3 votes

0 answers

93 views

If two homotopic maps $f,g: S^n \to Y$ agree on a disk $D$ containing basepoint, then $f,g$ are homotopic rel $D$.

algebraic-topology homotopy-theory

asked Oct 21, 2021 at 23:02

3 votes

0 answers

73 views

Homotopy groups of the higher dimensional Hawaiian Earring!

algebraic-topology homotopy-theory

asked Nov 3, 2021 at 16:39

3 votes

3 answers

106 views

Substitution in definite integral

calculus

asked Apr 20, 2016 at 16:06

3 votes

0 answers

91 views

Can this space retract to its boundary?

general-topology algebraic-topology

asked Jul 20 at 21:38

2 votes

1 answer

81 views

A Banach space cannot be countable union of its proper subspaces

functional-analysis banach-spaces baire-category

asked Mar 30, 2020 at 12:02

2 votes

2 answers

104 views

Show that $\sum_{r=0}^{n}\binom{n}{r}\binom{m+r}{n}= \sum_{r=0}^{n}\binom{n}{r}\binom{m}{r}2^r$

sequences-and-series binomial-coefficients

asked Jun 3, 2016 at 15:05

2 votes

1 answer

75 views

If $x_{n+1}= \frac{x_n^2+x_n+1}{x_n+1}$ find$ \sum_{n=1}^{p}\frac{1}{1+x_n}$

sequences-and-series

asked Nov 29, 2015 at 15:59

1 vote

1 answer

190 views

Find the distance between two points, given maximal angles subtended by them

geometry trigonometry

asked Jan 3, 2016 at 14:55

1 vote

2 answers

38 views

Given $\int _{-1}^{1}g(x)= 1$ show that $\int _{-1}^{1}f(x)g(x)\geq 1$ for certain $f,g$.

inequality definite-integrals

asked Apr 28, 2016 at 19:15

1 vote

0 answers

120 views

To find all functions $h:\mathbb{R}\to\mathbb{R}$ such that $h(x+y) = h(x)+h(y)$ and $h(xy)=h(x)h(y)$ [duplicate]

real-analysis functional-equations

asked Aug 14, 2016 at 7:39

1 vote

2 answers

47 views

Minimum number of elements in $S_A$, given $|A|=n$

combinatorics

asked May 19, 2016 at 7:30

1 vote

0 answers

26 views

Does this $n$-Ball 'grow' out of the unit box?

euclidean-geometry

asked May 19, 2017 at 16:51

1 vote

1 answer

33 views

Double mapping cone of coprime maps between circles.

general-topology algebraic-topology

asked Jul 20 at 21:07

1 vote

1 answer

72 views

Free action of Group $G$ on $S^n$ gives free resolution of $\mathbb{Z}$ as a $\mathbb{Z}[G]$-module.

algebraic-topology homology-cohomology geometric-topology group-cohomology

asked Oct 13, 2021 at 21:50

0 votes

1 answer

9k views

Can a non-continuous function be differentiable?

calculus derivatives

asked May 29, 2016 at 5:22

0 votes

0 answers

31 views

If $a(P)$ and $b(P)$ are no. of points on, and outside a convex polygon $P$, then $\sum x^{a(P)}(1-x)^{b(P)}=1 $ for all real $x$,

combinatorics geometry

asked Aug 26, 2016 at 12:03

0 votes

3 answers

924 views

diophantine equation: $x^2 +y^2 = z^n$ [duplicate]

number-theory induction

asked Nov 29, 2015 at 17:38

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30 Questions

Calculate $\int_{0}^{1} (x-f(x))^{2016} dx$, given $f(f(x))=x$.

domain of $x^x$

Cyclic system of cubic equations in $5$ variables

Given $a+b+..=a^7+b^7+..=0$ show that $a(a+b)..=0$ [duplicate]

Why was it necessary for the Riemann integral to consider all partitions and taggings?

One of the diagonals in a hexagon cuts of a triangle of area $\leq 1/6^{th}$ of the hexagon

For integer $n>2$, $(n!)^2 > n^n$ [duplicate]

Inequality involving integration [duplicate]

Partitioning of sets

$2^{49}$ ways to choose a set of integers $\leq 50$ with odd sum

Show that $\{a_n\}$ defined by $a_{n+1}=\frac{a_n+2}{a_n+1}$ converges

Number of labelled trees on $n$ vertices containing $2$ fixed non-adjacent edges

Automorphism group of finite $k$-algebra as an affine variety

If two homotopic maps $f,g: S^n \to Y$ agree on a disk $D$ containing basepoint, then $f,g$ are homotopic rel $D$.

Homotopy groups of the higher dimensional Hawaiian Earring!

Substitution in definite integral

Can this space retract to its boundary?

A Banach space cannot be countable union of its proper subspaces

Show that $\sum_{r=0}^{n}\binom{n}{r}\binom{m+r}{n}= \sum_{r=0}^{n}\binom{n}{r}\binom{m}{r}2^r$

If $x_{n+1}= \frac{x_n^2+x_n+1}{x_n+1}$ find$ \sum_{n=1}^{p}\frac{1}{1+x_n}$

Find the distance between two points, given maximal angles subtended by them

Given $\int _{-1}^{1}g(x)= 1$ show that $\int _{-1}^{1}f(x)g(x)\geq 1$ for certain $f,g$.

To find all functions $h:\mathbb{R}\to\mathbb{R}$ such that $h(x+y) = h(x)+h(y)$ and $h(xy)=h(x)h(y)$ [duplicate]

Minimum number of elements in $S_A$, given $|A|=n$

Does this $n$-Ball 'grow' out of the unit box?

Double mapping cone of coprime maps between circles.

Free action of Group $G$ on $S^n$ gives free resolution of $\mathbb{Z}$ as a $\mathbb{Z}[G]$-module.

Can a non-continuous function be differentiable?

If $a(P)$ and $b(P)$ are no. of points on, and outside a convex polygon $P$, then $\sum x^{a(P)}(1-x)^{b(P)}=1 $ for all real $x$,

diophantine equation: $x^2 +y^2 = z^n$ [duplicate]