Ian
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 16 Is this of any real importance to the mathematical scientific community? 16 Is $\sqrt[3]{p+q\sqrt{3}}+\sqrt[3]{p-q\sqrt{3}}=n$, $(p,q,n)\in\mathbb{N} ^3$ solvable? 13 Find all positive integers $n$ s.t. $3^n + 5^n$ is divisible by $n^2 - 1$ 13 Solve $x^2 + 8 = 3^n$, where $x\in\mathbb N$. 12 How to either prove or disprove if it is possible to arrange a series of numbers such the sum of any two adjacent number adds up to a prime number

Reputation (3,760)

 +15 If $3^x$ and $5^x$ are both integers, is $x$ an integer? +5 Solving the system $(18xy^2+x^3, 27x^2y+54y^3)=(12, 38)$ +15 Does a “cubic” matrix exist? +10 Differentiable $N$ times, $f'(x_{0})=\cdots=f^{(N-1)}(x_0)=0$, $f^{(N)}(x_0)>0\implies f$ increasing on $x_0$?

Questions (26)

 99 Does a “cubic” matrix exist? 34 Is there any geometric way to characterize $e$? 21 Mystery about $\sum_{n\geqslant 1}2^{-n!}$ 17 Rigorous proof that $\displaystyle\frac{1}{3} = 0.333\ldots$ 16 Evaluating $\sum_{k=1}^{\infty}\frac{\sin\left(k\theta\right)}{k^{2u+1}}$ with multiple integrals

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 44 calculus × 18 20 sequences-and-series × 15 36 algebra-precalculus × 16 18 summation × 9 29 diophantine-equations × 2 16 harmonic-numbers × 2 26 elementary-number-theory × 11 15 inequality × 3 25 number-theory × 12 14 trigonometry × 6

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