Intereting Posts

Can we make $\tan(x)$ arbitrarily close to an integer when $x\in \mathbb{Z}$?
Wanted: Low-dimensional SOS certificate for the AM-GM inequality
In naive set theory ∅ = {∅} = {{∅}}?
Prove that any polynomial in $F$ can be written in a unique manner as a product of irreducible polynomials in F.
Relation between Stiefel-Whitney class and Chern class
Co-countable Topology On Uncountable Set
The last few digits of $0^0$ are $\ldots0000000001$ (according to WolframAlpha).
Prove that the equation $x^4+(2k^2)x^2+2k^4$ is not a perfect square
Dot Product Intuition
Determine all primes $p$ for which $5$ is a quadratic residue modulo $p$
Multivariable Gauss's Lemma
Deriving the Airy functions from first principles
Example of Artinian module that is not Noetherian
Does this double series converge?
Integral domain, UFD and PID related problem

If $\;p=m+n$ where $p\in\mathbb P$, then $m,n$ are coprime, of course. But what about the converse?

Conjecture:

$p$ is prime if $\;\forall m,n\in\mathbb Z^+\!:\,p=m+n\implies \gcd(m,n)=1$

- How often does $D(n^2) = m^2$ happen, where $D(x)$ is the deficiency of $x$?
- Is it cheating to use the sign function when sieving for twin primes?
- Yet another conjecture about primes
- Does make sense a generalization of Lagarias equivalence with $H_n^s=1+1/2^s+\ldots+1/n^s$ and $\sigma^s(n)=\sum_{k\mid n}k^s$, for $\Re s>1$?
- What does proving the Collatz Conjecture entail?
- Symmetry of bicycle-lock numbers

Tested (and verified) for all $p<100000$.

- Does this category have a name? (Relations as objects and relation between relations as morphisms)
- Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$
- List of generally believed conjectures which cannot all be true
- Prove $\gcd(a+b,a^2+b^2)$ is $1$ or $2$ if $\gcd(a,b) = 1$
- Prove a set of nonnegative integers with greatest common divisor 1 and closed under addition has all but finite many nonnegative integers.
- Is it known or new?
- If $\gcd(a,b)=1$ , and $a$ is even and $b$ is odd then $\gcd(2^{a}+1,2^{b}+1)=1$?
- Can you define a greatest common divisor in a commutative ring that is not a domain?
- Every prime number divide some sum of the first $k$ primes.
- Prove that $\lim\limits_{x\to\infty} \frac{\Gamma(x+1,x(1+\epsilon))}{x\Gamma(x)}=0$.

It is true. Suppose $p\geqslant 2$ is *not* prime. Then we can write $p=xy$ with $x,y\geqslant 2$. Then we find $p=m+n$, with $m=x$ and $n=x(y-1)$. Those are obviously not coprime.

If $d \mid p$ and $d<p$, then $1 = \gcd(d, p-d) = \gcd(d, p) = d$, so $p$ is prime.

for p = 1 obviously wrong

(for all positive integers m, n with m+n=p (of course there are no ones, doesn’t matter) there is gcd(m,n)=1, but 1=p is not prime)

- This infinitely nested root gives me two answers $ \sqrt{4+\sqrt{8+\sqrt{32+\sqrt{512+\sqrt{\frac{512^2}{2}+\sqrt{…}}}}}} $
- How can a = x (mod m) have multiple meanings in modular arithmetic?
- Is a linear tranformation onto or one-to-one?
- Understanding the subdifferential sum rule
- Integrate $ \sin x /(1 + A \sin x)$ over the range $0$,$2 \pi$ for $A=0.2$
- Group Structure on $\Bbb R$
- Is $(\mathbf{V} \cap \mathbf{W})^{\bot}=(\mathbf{V}^{\bot} \cap \mathbf{W}^{\bot})$?
- A basic question on convergence in prob. and a.s. convergence
- integrals proving equality
- Morphisms of $k$-schemes who agree on $\overline{k}$-points.
- Infinite set and proper subset.
- Proof that $q^2$ is indivisible by 3 if $q$ is indivisible by 3.
- diophantine equation: $x^2 +y^2 = z^n$
- Properties of special rectangle (measure)
- Straight lines – product of slope of perpendicular lines.