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21 votes
2 answers
3k views

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

15 votes
1 answer
9k views

domain of $x^x$

9 votes
1 answer
158 views

Cyclic system of cubic equations in $5$ variables

8 votes
1 answer
177 views

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

8 votes
2 answers
976 views

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

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

5 votes
5 answers
239 views

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

4 votes
0 answers
29 views

Inequality involving integration [duplicate]

4 votes
3 answers
322 views

Partitioning of sets

3 votes
2 answers
356 views

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

3 votes
4 answers
227 views

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

3 votes
3 answers
763 views

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

3 votes
1 answer
158 views

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

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 $D$.

3 votes
0 answers
73 views

Homotopy groups of the higher dimensional Hawaiian Earring!

3 votes
3 answers
106 views

Substitution in definite integral

3 votes
0 answers
91 views

Can this space retract to its boundary?

2 votes
1 answer
81 views

A Banach space cannot be countable union of its proper subspaces

2 votes
2 answers
104 views

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

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}$

1 vote
1 answer
190 views

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

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 $f,g$.

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]

1 vote
2 answers
47 views

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

1 vote
0 answers
26 views

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

1 vote
1 answer
33 views

Double mapping cone of coprime maps between circles.

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.

0 votes
1 answer
9k views

Can a non-continuous function be differentiable?

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 $x$,

0 votes
3 answers
924 views

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