20 Prove 24 divides $u^3-u$ for all odd natural numbers $u$ 15 Quaternions: why does ijk = -1 and ij=k and -ji=k 14 Prove that $\sqrt{3}+ \sqrt{5}+ \sqrt{7}$ is irrational 9 With a product and sum of $x$ and $y$, calculate $9x^2+15y^2$ 6 $f:\mathbb R \rightarrow \mathbb R$ be differentiable function such that $f'(x)$ is continuous and $f(x+1)=f(x)+1$ for all $x \in\mathbb R$.

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### Questions (13)

 4 Computer Assisted proofs apart from the 4 color theorem 3 Why does a Penrose Stair seem to be correct? 3 limit of 'exponential type' sequences 3 Integrals of the form $\int \frac{f(x)}{x^p \pm 1}$ or $\int \frac{f(x)}{e^x\pm 1}$ 2 Given four numbers $(a,b,e,n)$ is it possible to find $k$ such that $k^{e}a = b \pmod n$?

### Tags (76)

 25 elementary-number-theory × 5 14 radicals 20 divisibility 14 rationality-testing 20 natural-numbers 8 linear-algebra × 8 15 quaternions 7 calculus × 6 14 algebra-precalculus × 3 7 real-analysis × 2

### Bookmarks (51)

 1173 Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio? 663 What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) [closed] 585 Examples of patterns that eventually fail 361 Can every proof by contradiction also be shown without contradiction? 215 How to check if a point is inside a rectangle?

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