Diophantine « 0,1,2,3,…

Filed under: Diophantine,Zahlentheorie — abi007 @ 9:09 pm

$\displaystyle x^p-y^q=1, x,y,p,q>1 \rightarrow 3^2-2^3=1$

$\displaystyle a\in\mathbb{Z}, p\in\mathbb{P}\rightarrow$
$\displaystyle a^p \equiv a \pmod{p}\,\!$

$\displaystyle \pi(x)\sim\frac{x}{\ln x}$

$\displaystyle Li(n)=\int_2^n\frac{dx}{ln(x)}\sim\pi(n)$

$\displaystyle \forall n>1\exists p\in\mathbb{P}:n<p<2n$

$\displaystyle (\frac{p}{q})(\frac{q}{p})=(-1)^{\frac{(p-1)(q-1)}{4}}$

$\displaystyle a^4+4b^4=(a^2+2b^2+2ab)(a^2+2b^2-2ab)$

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