Question

Given positive numbers $x_1,...,x_n$ such that $x_1\cdots x_n=1$ prove that $\frac{1}{n-1+x_1}+\cdots+\frac{1}{n-1+x_n}\le 1$

score 685 · Answer 1 · 2026-04-16 14:50:06

685

Views

Given positive numbers $x_1,...,x_n$ such that $x_1\cdots x_n=1$ prove that $\frac{1}{n-1+x_1}+\cdots+\frac{1}{n-1+x_n}\le 1$

Published on 16 Apr 2026 - 14:50

score 101 · Answer 2 · 2026-04-13 08:28:42

101

Views

What is the value of $1^z$ for $z\in\mathbb{C}$?

Published on 13 Apr 2026 - 8:28

score 365 · Answer 3 · 2026-04-14 22:53:56

365

Views

Is there a function that is both exponential or linear at one end and then logarithmic at the other (joining two types of functions generally)

Published on 14 Apr 2026 - 22:53

score 168 · Answer 4 · 2026-04-13 05:22:25

168

Views

Is $z^w$ for $z,w \in \mathbb{C}$ well-defined if you don't take a branch cut?

Published on 13 Apr 2026 - 5:22

score 43 · Answer 5 · 2026-04-16 00:39:18

43

Views

Can it be proven that a product of factors where two or more factors have non-integer exponentiation is a irrational number?

Published on 16 Apr 2026 - 0:39

score 250 · Answer 6 · 2026-04-11 15:01:44

250

Views

Here is another "$e$-$\pi$-without -calculating" comparison

Published on 11 Apr 2026 - 15:01

score 98 · Answer 7 · 2026-04-13 08:07:43

98

Views

Fake proof that $\sqrt{i} = 1$

Published on 13 Apr 2026 - 8:07

score 2.1k · Answer 8 · 2026-04-12 13:39:51

2.1k

Views

Sigmoid Curve function calculation

Published on 12 Apr 2026 - 13:39

score 42 · Answer 9 · 2026-04-17 02:12:43

42

Views

Where does the identity $p^{-ns}=s\int_{p^n}^\infty x^{-s-1}dx$ come from?

Published on 17 Apr 2026 - 2:12

score 31 · Answer 10 · 2026-04-15 06:18:21

31

Views

Simplifying polynomials to a variable power

Published on 15 Apr 2026 - 6:18

score 859 · Answer 11 · 2026-04-16 12:58:18

859

Views

Solving the equation $(x^2-7x+11)^{(x^2-13x+42)} = 1$

Published on 16 Apr 2026 - 12:58

score 434 · Answer 12 · 2026-04-13 02:08:28

434

Views

Adding decreasing power of the same number

Published on 13 Apr 2026 - 2:08

score 94 · Answer 13 · 2026-04-19 20:34:40

94

Views

Find n where $(2n+1)2^{4n+5} = 3 \pmod{7}$

Published on 19 Apr 2026 - 20:34

score 324 · Answer 14 · 2026-04-11 06:55:31

324

Views

Value of $i^\sqrt3$

Published on 11 Apr 2026 - 6:55

score 252 · Answer 15 · 2026-04-12 03:28:38

252

Views

Can all naturals can be expressed as sums of prime powers of $\{3,5,7,13\}$?

Published on 12 Apr 2026 - 3:28

List Question

Given positive numbers $x_1,...,x_n$ such that $x_1\cdots x_n=1$ prove that $\frac{1}{n-1+x_1}+\cdots+\frac{1}{n-1+x_n}\le 1$

What is the value of $1^z$ for $z\in\mathbb{C}$?

Is there a function that is both exponential or linear at one end and then logarithmic at the other (joining two types of functions generally)

Is $z^w$ for $z,w \in \mathbb{C}$ well-defined if you don't take a branch cut?

Can it be proven that a product of factors where two or more factors have non-integer exponentiation is a irrational number?

Here is another "$e$-$\pi$-without -calculating" comparison

Fake proof that $\sqrt{i} = 1$

Sigmoid Curve function calculation

Where does the identity $p^{-ns}=s\int_{p^n}^\infty x^{-s-1}dx$ come from?

Simplifying polynomials to a variable power

Solving the equation $(x^2-7x+11)^{(x^2-13x+42)} = 1$

Adding decreasing power of the same number

Find n where $(2n+1)2^{4n+5} = 3 \pmod{7}$

Value of $i^\sqrt3$

Can all naturals can be expressed as sums of prime powers of $\{3,5,7,13\}$?

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