query: Estimating $|a+b|^p$ for real $p$.
positive_passages.docid: 30386
positive_passages.text: Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
negative_passages.docid: 88059
negative_passages.text: Elementary central binomial coefficient estimates
negative_passages.docid: 129536
negative_passages.text: Asymptotic behaviour of sums of consecutive powers
negative_passages.docid: 145884
negative_passages.text: Showing $\left|\frac{a+b}{2}\right|^p+\left|\frac{a-b}{2}\right|^p\leq\frac{1}{2}|a|^p+\frac{1}{2}|b|^p$
negative_passages.docid: 52249
negative_passages.text: Is it true that $||a|^p - |b|^p| \le C_p|a - b|^p$ for $1 < p < \infty$?
negative_passages.docid: 128608
negative_passages.text: Closed form for the series $a+a^p+(a^p)^p+\dots$
negative_passages.docid: 125707
negative_passages.text: A simple proof (hopefully) for $2^x \neq 0$
negative_passages.docid: 102234
negative_passages.text: Show $a^p \equiv a \mod 2p$
negative_passages.docid: 151961
negative_passages.text: Irreducibility of $x^{p(p-1)}+x^{p(p-2)}+\cdots+x^p+1$ over $\mathbb Q$
negative_passages.docid: 66610
negative_passages.text: Finding a correspondence between $\{0,1\}^A$ and $\mathcal P(A)$
negative_passages.docid: 20526
negative_passages.text: Show that $PF.PG=b^2$ in a hyperbola
negative_passages.docid: 130281
negative_passages.text: Proving $a^ab^b + a^bb^a \le 1$, given $a + b = 1$
negative_passages.docid: 102717
negative_passages.text: Real analysis of powers
negative_passages.docid: 55509
negative_passages.text: Factor a polynomial over the reals
negative_passages.docid: 14221
negative_passages.text: How can we prove it? ${a}{b}≤\frac{a^p}{p}+\frac{b^q}{q}$
negative_passages.docid: 25623
negative_passages.text: Does $\sqrt{a+b} \le \sqrt a + \sqrt b$ hold for all positive real numbers a and b?
negative_passages.docid: 6332
negative_passages.text: If $p\equiv1\mod{4}$, then $p=a^{2}+b^{2}$ where a and b are uniquely determined