Douglas B. Staple
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1,763
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 14 Examples of apparent patterns that eventually fail 12 Second part of the factorial sum divisibility question 10 Minimum of $n$? $123456789x^2 - 987654321y^2 =n$ ($x$,$y$ and $n$ are positive integers) 8 Find a composite number $n$ satisfies $(2+3I)^n≡2-3I\pmod{n}$ 6 Second part of the factorial sum divisibility question

### Reputation (1,763)

 +20 Algebra: Best mental images +20 Prove that $\sum_{k=0}^n{e^{ik^2}} = o(n^\alpha)$, $\forall \alpha >0$ +10 Estimation of the number of prime numbers in a $b^x$ to $b^{x + 1}$ interval +5 Strange notation for a decimal expansion of a transcendental number

### Questions (8)

 3 $y - y_0 = \frac{d^2}{dx^2}\left[ \ln\left( \frac{y}{y_0} \right) \right]$, solve for $y$. 2 $\sum_{k=1}^n m(k)$, where $m(k)$ is defined by $2^{m(k)} || k$. 1 Strange notation for a decimal expansion of a transcendental number 1 Asymptotic expansion for $\frac{1}{2\zeta(3)}\int_x^\infty \frac{u^2}{e^u - 1} du$? 0 “Dependence” or “dependencies” of a function on multiple variables.

### Tags (57)

 28 elementary-number-theory × 9 9 group-theory × 3 25 number-theory × 6 8 real-analysis × 4 13 diophantine-equations × 2 8 algebraic-number-theory 11 modular-arithmetic × 3 7 calculus × 2 9 abstract-algebra × 3 6 prime-numbers × 2

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