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Mathematics
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sku
  • Member for 8 years, 2 months
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10
An interesting finding on twin primes
Nov 2, 2023
9
show that $(n+1)(n+2)...(2n)$ is divisible by $2^n$ but not by $2^{n+1}$
Apr 29, 2017
8
Prove $a^2 + b^2 + c^2 + ab + bc +ca \ge 6$ given $a+b+c = 3$ for $a,b,c$ non-negative real.
Jul 27, 2021
7
Conjecture: $\sum\limits_{k=1}^nk^m=S_3(n)\times\frac{P_{m-3}(n)}{N_m}$ for odd $m>1 \ ;\ =S_2(n)\times\frac{P_{m-2}'(n)}{N_m}$ for even $m$.
Dec 17, 2023
7
Intuition behind $\phi(n) = \sum\limits_{d\mid n}\mu(d)\frac{n}{d}$
Jun 17, 2017
5
Proof of product rule for limits
Mar 3, 2018
5
Given $z^2-1\mid x^2z^2-1$, prove $\frac{x^2z^2-1}{z^2-1}$ is never prime, for $x$, $z$ integers such that $x>z>1$.
Mar 23, 2022
4
Prove that $\sum_{n = 1}^{n = s} n^2 \ne \sum_{n = t}^{n = u} n^2$
Apr 21, 2017
4
show that $\sum_{i = 1}^{2k}\frac{ (-1)^{i+1}}{i} = \sum_{i = k+1}^{2k} \frac{1}{i}$
Apr 30, 2017
4
How does $\frac{2\sqrt{7}}{3}\cos\left (\frac13\arccos\frac{1}{2\sqrt{7}}\right)+\frac23$ simplify to $1+2\cos\frac{2\pi}{7}$?
Jul 14, 2023
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Is simple mathematics for learners allowed here?
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51
Why doesn't the nuclear fusion in a star make it explode?
11
What happens when the universe runs out of fuel?
8
A gedanken on being able to navigate back to Earth