ElementX

### Questions (35)

 6 Prove that there are infinitely many composite number $m$ such that $a^{m-1} - 1$ is divisible by $m$ 5 A problem regarding a sequence in $C[0;1]$ 4 Find a field $F$ such that $[F : \mathbb{Q}] = 3$ and $F \ne \mathbb{Q }(\sqrt[3]{a}), \forall a \in \mathbb{Q}$ 4 Prove that $(C^1[0,1], ||.||)$ is not a Banach space 3 If $x^p - x - a$ has no root in $F$ then $x^p - x - a$ is irreducible in $F$ with $F$ is a field with char $p$

### Reputation (434)

 +25 Is $B_1$ a subspace of $\mathbb{C}^3$? +5 Find a field $F$ such that $[F : \mathbb{Q}] = 3$ and $F \ne \mathbb{Q }(\sqrt[3]{a}), \forall a \in \mathbb{Q}$ +15 Can an unbounded sequence have a lower bound and no upper bound (and vice versa)? +5 About two functions whose Lebesgue integral on all sets of a $\sigma-$algebra are equal

 1 Can an unbounded sequence have a lower bound and no upper bound (and vice versa)? 1 Is $B_1$ a subspace of $\mathbb{C}^3$?

### Tags (38)

 1 sequences-and-series × 3 1 vector-analysis 1 real-analysis × 2 1 vectors 1 proof-verification × 2 0 field-theory × 6 1 vector-spaces × 2 0 functional-analysis × 6 1 linear-algebra 0 extension-field × 4

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