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Sep
14
comment on a recursive sequence (exercise 8.14 Apostol).
I don't think I will spoil anything be mentioning that the $b_n$ are what is called the Fibonacci numbers, and what you are told is to find the limit of consecutive quotients.
Sep
9
comment How prove there exist prime numbers $P_{1},P_{2},\cdots,P_{n}$ such $P_{k}\mid c+k$
This is apparently related to Grimm's conjecture which is an open problem?
Sep
9
comment How prove there exist prime numbers $P_{1},P_{2},\cdots,P_{n}$ such $P_{k}\mid c+k$
Can you elaborate? Suppose we consider $n=3$ and look at the numbers $30,31,32$. If from $30$ we pick $p_1=2$ (unfortunate?) and to $31$ we use $p_2=31$, then when trying to pick a $p_3$ from $32$ we are in trouble.
Sep
9
awarded  Organizer
Sep
9
revised How prove there exist prime numbers $P_{1},P_{2},\cdots,P_{n}$ such $P_{k}\mid c+k$
the tag was interpreted as two independent tags
Sep
9
suggested suggested edit on How prove there exist prime numbers $P_{1},P_{2},\cdots,P_{n}$ such $P_{k}\mid c+k$
Sep
9
answered Easy question about an equivalence relation
Sep
9
comment Are groups satisfying $g=g^{-1}$ for all $g \in G$ abelian?
Further hint: $xy = (xy)^{-1} = \dots = yx$.
Sep
9
comment Are groups satisfying $g=g^{-1}$ for all $g \in G$ abelian?
See also Group where every element is order 2 and the threads linked to it.
Sep
9
comment Are groups satisfying $g=g^{-1}$ for all $g \in G$ abelian?
Not clear how your attempt is meant to work. You need to prove that the group (you know it is a group, so you know inverses exist) is abelian. Or else, you need to come up with an example where $g=g^{-1}$ for all $g$ and the group is not abelian. Which one did you attempt?
Sep
7
comment How many binary sequences of length 16 have exactly eight 1’s?
Yes, more or less by definition, it is $_{16}C_8$ or $\tbinom{16}{8}$.
Sep
7
comment How many binary sequences of length 16 have exactly eight 1’s?
You know about "combinations" a.k.a. binomial coefficients, like $\tbinom{16}{8}$?
Sep
6
comment Do the functions periodic with period $1$ a vector space?
@MichaelAlbanese This is an interesting comment. The closedness under addition depends on this. Must $1$ be the (shortest) period, or is it enough that $1$ is a period?
Sep
6
comment Prove that the set $\{(x,y) \in\mathbb R^2\mid 2<x^2+y^2<4\}$ is an open set
It is possible that the relation between continuity and open sets is not yet known when you are told to solve problems like this.
Sep
6
comment Prove that the set $\{(x,y) \in\mathbb R^2\mid 2<x^2+y^2<4\}$ is an open set
Sounds like one correct approach. Should use $\sqrt{4}-\sqrt{x^2+y^2}$ and $\sqrt{x^2+y^2}-\sqrt{2}$ when you define your $\delta$, though. If that little ball was not included in your annulus $S$, pick a point that "witnesses" this, and use the triangle inequality involving that point and $(x,y)$ and $(u,v)$.
Sep
6
comment Does the analytic continuation of $f$ always exist?
Yes. Your link also refers the Wikipedia page lacunary function with more information.
Sep
6
answered Does the analytic continuation of $f$ always exist?
Sep
6
comment Consecutive Prime Gap Sum (Amateur)
@AlonsodelArte Question was updated. The sequence is A040998.
Sep
5
comment Proof of infinitely many rationals “close” to a rational
Shouldn't it be $b \ne 0$?
Sep
5
revised Series $\sum_{n=0}^{\infty}\frac{1}{2^n-1+e^x}$ properties
deleted 2 characters in body