List questions from solution-verification

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$K(\zeta)/k(\zeta)$ is Galois (proof verification)

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Finite numbers that cannot be represented with $4m+7k$ using complete induction

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we want to prove that $(n,n+1) \cap \mathbb{N}$ is empty

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PROPOSED PROOF for: If $p$ is a prime number such that $p|ab$, then $p|a$ or $p|b$.

Proof by induction check

For periodic $f,g$ (and continuous), does $\lim (f-g) = 0 $ imply $f=g$?

Is this solution of martingale problem correct?

Verifying that the identity functor is indeed a functor

On the ring $\frac{\mathbb{Q}[x]}I$ , where $I=\langle x^2-x\rangle$

Isomorphism between $S_n$ and a subgroup of $S_{n+1}$

Projection on $U$ along $W$ with $U,W$ contained in $V=U\oplus W$

Limiting probability of $m$ cells having $k$-tuple occupancy when $r$ balls are distributed into $n$ cells (from Feller Vol I)

Area relations of a parabolic segment

Totally bounded set in a metric space $\implies$ bounded

Points A, B and C have position vectors a = i + 2 j, b = 2i + j and c = 2i − 3 j. Find the shortest distance from B to line AC

$K(\zeta)/k(\zeta)$ is Galois (proof verification)

Finite numbers that cannot be represented with $4m+7k$ using complete induction

we want to prove that $(n,n+1) \cap \mathbb{N}$ is empty

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