Question

Linear Algebra composition Can someone help ( Challenge Problem )

score 44 · Answer 1 · 2019-10-30 07:37:30

44

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Linear Algebra composition Can someone help ( Challenge Problem )

Published on 30 Oct 2019 - 7:37

score 82 · Answer 2 · 2026-03-25 21:54:05

82

Views

If $q^k n^2$ is an odd perfect number with special prime $q$, is it true that $\sigma(n^2)/q^k \mid n^2$?

Published on 25 Mar 2026 - 21:54

score 33 · Answer 3 · 2019-11-01 15:26:26

33

Views

Are there other ways to solve uniqueness theorems?

Published on 01 Nov 2019 - 15:26

score 807 · Answer 4 · 2019-11-02 11:02:07

807

Views

Finding the locus of the centre of the circle which is orthogonal to a family of circles

Published on 02 Nov 2019 - 11:02

score 127 · Answer 5 · 2019-11-03 08:09:15

127

Views

Finding the range of radius of a family of circles when they pass through a fixed point and have $x$-axis as their tangent

Published on 03 Nov 2019 - 8:09

score 39 · Answer 6 · 2019-11-03 17:38:45

39

Views

A question about open set.

Published on 03 Nov 2019 - 17:38

score 88 · Answer 7 · 2019-11-04 10:35:37

88

Views

Prove that if $A ≠ \emptyset$ and $f: A \rightarrow A$ and for all $g: A \rightarrow A$, $f \circ g = f$, then $f$ is a constant function.

Published on 04 Nov 2019 - 10:35

score 203 · Answer 8 · 2026-03-26 06:12:49

203

Views

Is there a simple proof that $\cos(1)$ is transcendental?

Published on 26 Mar 2026 - 6:12

score 1.1k · Answer 9 · 2019-11-07 03:00:32

1.1k

Views

Show $f(x)=2x \sin{\frac{1}{x} -\cos{\frac{1}{x}}}$ is discontinuous at $0$

Published on 07 Nov 2019 - 3:00

score 900 · Answer 10 · 2026-03-29 13:23:49

900

Views

Prove that if p and q are both prime numbers, with p > q > 2, then $p^4− q^4$ is divisible by 16

Published on 29 Mar 2026 - 13:23

score 627 · Answer 11 · 2026-03-26 22:58:25

627

Views

Prove $\int_0^1\frac{x^{2n}}{1+x}dx=\ln2+H_n-H_{2n}$

Published on 26 Mar 2026 - 22:58

score 1.2k · Answer 12 · 2019-11-09 19:10:24

1.2k

Views

Easier proof of Tietze theorem in metric case.

Published on 09 Nov 2019 - 19:10

score 45 · Answer 13 · 2019-11-10 07:18:42

45

Views

Suppose $f,g,h$ are functions. Prove $f \circ (g \circ h) = (f\circ g) \circ h $

Published on 10 Nov 2019 - 7:18

score 499 · Answer 14 · 2019-11-10 10:11:01

499

Views

Symmetric set difference and odd number of sets containing x

Published on 10 Nov 2019 - 10:11

score 189 · Answer 15 · 2019-11-10 23:50:58

189

Views

If $f$ has a continuous second derivative, prove that $f(x) = f(0) + f'(0) + \int_0^x (x-t)f''(t)dt$.

Published on 10 Nov 2019 - 23:50

List Question

Linear Algebra composition Can someone help ( Challenge Problem )

If $q^k n^2$ is an odd perfect number with special prime $q$, is it true that $\sigma(n^2)/q^k \mid n^2$?

Are there other ways to solve uniqueness theorems?

Finding the locus of the centre of the circle which is orthogonal to a family of circles

Finding the range of radius of a family of circles when they pass through a fixed point and have $x$-axis as their tangent

A question about open set.

Prove that if $A ≠ \emptyset$ and $f: A \rightarrow A$ and for all $g: A \rightarrow A$, $f \circ g = f$, then $f$ is a constant function.

Is there a simple proof that $\cos(1)$ is transcendental?

Show $f(x)=2x \sin{\frac{1}{x} -\cos{\frac{1}{x}}}$ is discontinuous at $0$

Prove that if p and q are both prime numbers, with p > q > 2, then $p^4− q^4$ is divisible by 16

Prove $\int_0^1\frac{x^{2n}}{1+x}dx=\ln2+H_n-H_{2n}$

Easier proof of Tietze theorem in metric case.

Suppose $f,g,h$ are functions. Prove $f \circ (g \circ h) = (f\circ g) \circ h $

Symmetric set difference and odd number of sets containing x

If $f$ has a continuous second derivative, prove that $f(x) = f(0) + f'(0) + \int_0^x (x-t)f''(t)dt$.

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