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Mathematics
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gareth618
  • Member for 6 years, 3 months
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question
15
Prove that there is no positive integer $n$ such that $1^{2000} + 2^{2000} + \ldots + n^{2000}$ is prime.
Jul 19, 2018
question
6
Find the value of $S$ in term of $k$ (telescoping sums)
Jun 3, 2018
question
3
If $x, y \in \mathbb{N^{*}}$, such that $\frac{x}{y}+\frac{y}{x} \in \mathbb{N}$, show that $x=y$. [duplicate]
Jun 23, 2018
question
3
For any $n \in \mathbb{N}$, show that: $\frac{1}{n+1} + \frac{1}{n+2} + \ldots + \frac{1}{2n} < \frac{5}{6}$.
Jun 25, 2018
question
3
Minimum of $\left(a + b + c + d\right)\left(\frac{1}{a} + \frac{1}{b} + \frac{4}{c} + \frac{16}{d}\right)$
Jul 19, 2018
question
3
$n^2 - n + 11$ is the product of four prime numbers, some of which may be the same. What is the minimum value of $n$?
Sep 7, 2018
question
3
If $2^t = a^b \pm 1$, what are all the possible values of $t$?
Sep 7, 2018
question
3
Find the nature of $\sum_{n = 1}^\infty \frac{1}{e \cdot \sqrt{e} \cdot \sqrt[3]{e} \cdots \sqrt[n]{e}}$
Oct 26, 2020
question
2
If $abc=1$, prove that $\frac{2}{(a+1)^2+b^2+1} + \frac{2}{(b+1)^2+c^2+1} + \frac{2}{(c+1)^2+a^2+1} \le 1$.
Jul 17, 2018
question
2
Let $R_n = \underbrace{11\ldots1}_{n}$. Prove that if $(n, m) = 1$, then $(R_n, R_m) = 1$.
Jul 29, 2018