Derek Luna's user avatar
Derek Luna's user avatar
Derek Luna's user avatar
Derek Luna
  • Member for 5 years, 8 months
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3 votes
2 answers
128 views

Is this a bijection from $[0,1)$ to $(0,1)$?

2 votes
1 answer
77 views

Baby Rudin Chapter $4$ Exercise $1$

2 votes
0 answers
180 views

Prove that if $x$ is element of the group G then $H = \lbrace x^n : n \in Z\rbrace$ is a subgroup of $G$.

2 votes
1 answer
90 views

Rigor in elementary number theory

1 vote
0 answers
35 views

Relatively prime integers and order of an integer [duplicate]

1 vote
2 answers
152 views

Let $S$ be the subset of $M(\mathbb{R})$ consisting of matrices of the form:

1 vote
1 answer
58 views

Show bijection of sets using calculus

1 vote
1 answer
1k views

Prove that $n!+1$ and $(n+1)!+1$ are relatively prime for every positive integer $n$.

1 vote
0 answers
56 views

Proof Verification for GTM Hungerford Ch $3.1$ #$13$

1 vote
0 answers
86 views

John Tate's Doctoral Thesis

1 vote
2 answers
41 views

Let $1< m,n \in \Bbb N$. The map $g: \Bbb Z_{m} \to \Bbb Z_{mk}$ given by $x \mapsto kx$ is a monomorphism

1 vote
1 answer
370 views

If $p$ is a prime satisfying $n<p<2n$ then $\binom{2n}{n}\equiv 0 \pmod p$.

1 vote
1 answer
343 views

Is the contrapositive of a true statement always provable?

1 vote
1 answer
609 views

Putnam and Beyond #3

1 vote
1 answer
57 views

Are there infinitely $M$ such that $\{\sqrt{M+2}\}=\{\sqrt{M}\}+1$? (where $\{x\}$ is the closest integer function)

0 votes
1 answer
222 views

Find a polynomial $p$ of degree $3$ such that $-1,2$,and $3$ are zeroes of $p$ and $p(0)=1$ where book solution lacks rigour.

0 votes
2 answers
59 views

Hungerford and the Well Ordering Principle

0 votes
1 answer
43 views

Show that $\begin{bmatrix}R&R\\0&R\end{bmatrix} \cong \begin{bmatrix}R&0\\R&R\end{bmatrix}$ for any ring $R$.

0 votes
1 answer
53 views

Let $r,s \in R$ where $R$ is a ring. Then $(mr)(ns)$ = $mn(rs)$ for all integers $m$ and $n$.

0 votes
1 answer
309 views

Show that a group $G$ is abelian if $(gh)^3 = g^3h^3$, $(gh)^4 = g^4h^4$, and $(gh)^5 = g^5h^5$ for all $g$ and $h$ in $G$. [duplicate]

0 votes
1 answer
512 views

Let $p$ be prime and $a$ an integer not divisible by $p$. Prove that if $a^{2^{n}} \equiv -1 \pmod p$, then $a$ has order $2^{n+1}$ modulo $p$. [duplicate]

0 votes
0 answers
52 views

Complete residue systems of $k$th powers reducing "in order".

0 votes
3 answers
62 views

Positively confused about negation

0 votes
0 answers
54 views

Cyclic subgroups and generator 1

0 votes
1 answer
112 views

Show that $U_{26}/\langle 5\rangle$ is isomorphic to $\mathbb{Z}_3$.

-1 votes
1 answer
62 views

Determine that a series is rational [closed]