Question

Is $(1+c^2)^n-\lfloor(1+c^2)^{n/2}\rfloor^2<(1+c^2)^{(n+1)/2}$ true for all integers $c>1$, when $n$ is an odd integer?

score 79 · Answer 1 · 2022-05-18 19:52:12

79

Views

Is $(1+c^2)^n-\lfloor(1+c^2)^{n/2}\rfloor^2<(1+c^2)^{(n+1)/2}$ true for all integers $c>1$, when $n$ is an odd integer?

Published on 18 May 2022 - 19:52

score 107 · Answer 2 · 2022-06-02 16:22:18

107

Views

How can I find natural number solutions to $\frac{186-x}{11x+1}=y$?

Published on 02 Jun 2022 - 16:22

score 51 · Answer 3 · 2026-03-26 17:14:05

51

Views

Can $c^2(a\cdot b)+c(a+b)=2^c-2$ be solved to find $\mathbb{N}$ solutions?

Published on 26 Mar 2026 - 17:14

score 232 · Answer 4 · 2026-03-27 15:06:32

232

Views

How does Wolfram Alpha find polynomial equation of given roots?

Published on 27 Mar 2026 - 15:06

score 54 · Answer 5 · 2022-06-03 17:15:41

54

Views

How fast can a series of positive rationals converge if we know its limit is rational?

Published on 03 Jun 2022 - 17:15

score 126 · Answer 6 · 2022-07-05 10:43:28

126

Views

Approximating reals by p-smooth ratios

Published on 05 Jul 2022 - 10:43

score 63 · Answer 7 · 2022-08-05 03:57:05

63

Views

Rational distances to 3 points in ${\bf R}^2$

Published on 05 Aug 2022 - 3:57

score 121 · Answer 8 · 2026-03-26 11:18:28

121

Views

Simple estimation of separation of powers of 2 and powers of 3?

Published on 26 Mar 2026 - 11:18

score 60 · Answer 9 · 2022-08-15 05:04:26

60

Views

Approximating a number by using only a given set of prime-factors for the approximant.

Published on 15 Aug 2022 - 5:04

score 40 · Answer 10 · 2026-02-23 06:04:04

40

Views

Showing that linear fractional equivalences preserve the irrationality measure

Published on 23 Feb 2026 - 6:04

score 73 · Answer 11 · 2026-02-23 06:05:27

73

Views

Why does $|x-p/q|\ge\frac{C(x)}{q^a}$ for all $p/q$ imply: "$|x-p/q|\lt\frac{1}{q^a}$ has only finitely many solutions"?

Published on 23 Feb 2026 - 6:05

score 80 · Answer 12 · 2022-08-19 00:27:17

80

Views

Least upper bound on $x_n = \min{|a - b\sqrt{3}| : a + b = n}$.

Published on 19 Aug 2022 - 0:27

score 67 · Answer 13 · 2022-09-01 17:06:34

67

Views

Reference request: A. Schinzel on digital sums of powers

Published on 01 Sep 2022 - 17:06

score 91 · Answer 14 · 2022-09-06 12:54:02

91

Views

Reduction step in the proof of Roth's theorem

Published on 06 Sep 2022 - 12:54

score 63 · Answer 15 · 2022-09-14 11:25:11

63

Views

Growth rate of $|a^n+b^n|$ where $a,b=(1\pm\sqrt{-7})/2$.

Published on 14 Sep 2022 - 11:25

List Question

Is $(1+c^2)^n-\lfloor(1+c^2)^{n/2}\rfloor^2<(1+c^2)^{(n+1)/2}$ true for all integers $c>1$, when $n$ is an odd integer?

How can I find natural number solutions to $\frac{186-x}{11x+1}=y$?

Can $c^2(a\cdot b)+c(a+b)=2^c-2$ be solved to find $\mathbb{N}$ solutions?

How does Wolfram Alpha find polynomial equation of given roots?

How fast can a series of positive rationals converge if we know its limit is rational?

Approximating reals by p-smooth ratios

Rational distances to 3 points in ${\bf R}^2$

Simple estimation of separation of powers of 2 and powers of 3?

Approximating a number by using only a given set of prime-factors for the approximant.

Showing that linear fractional equivalences preserve the irrationality measure

Why does $|x-p/q|\ge\frac{C(x)}{q^a}$ for all $p/q$ imply: "$|x-p/q|\lt\frac{1}{q^a}$ has only finitely many solutions"?

Least upper bound on $x_n = \min{|a - b\sqrt{3}| : a + b = n}$.

Reference request: A. Schinzel on digital sums of powers

Reduction step in the proof of Roth's theorem

Growth rate of $|a^n+b^n|$ where $a,b=(1\pm\sqrt{-7})/2$.

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