10 What is an example of a proof by minimal counterexample? 9 If $A$ is dense in $\Bbb Q$, then it must be dense in $\Bbb R$. 7 Proving convergence of a bizarre sequence 5 Are there infinitely many prime numbers of the form $p^2+4$ with $p$ prime? 4 How many integer solutions are there on an $n$ dimensional hypersphere of radius $\sqrt{r}$ centered at the origin?

### Reputation (2,019)

 +58 What's the sum of the reciprocals of the numbers that can be written as the sum of two positive cubes? +2 Regarding proving a $\sigma$ algebra is equal smallest $\sigma$ algebra containing a algebra. +2 The sum of infinite series $(1/2)(1/5)^2 + (2/3)(1/5)^3 + (3/4)(1/5)^4…$ +10 Exploiting a Diophantine approximation of $\pi^4$ into giving a series of rationals for $\pi^4$

### Questions (38)

 27 Constructing an infinite chain of subfields of 'hyper' algebraic numbers? 18 Exploiting a Diophantine approximation of $\pi^4$ into giving a series of rationals for $\pi^4$ 11 What's the sum of the reciprocals of the numbers that can be written as the sum of two positive cubes? 11 Proving $\int_0^r{(r^m-x^m)^{1/m}dx}=\frac{\Gamma\left(\frac{1}{m}+1\right)\Gamma\left(\frac{1}{m}+1\right)}{\Gamma\left(\frac{2}{m}+1\right)}r^2$ 8 On the sets of sums $\sum\limits_{n=1}^\infty\frac{a_n}{n^s}$ with $(a_n)$ periodic and integer valued, for different values of $s$ natural number

### Tags (123)

 23 real-analysis × 18 10 number-theory × 10 16 sequences-and-series × 33 10 calculus × 9 13 proof-writing × 8 10 infinite-descent 11 proof-verification × 10 10 examples-counterexamples 10 elementary-number-theory × 12 9 real-numbers

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