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mikespivey.wordpress.com | ||
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pfzhang.wordpress.com
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| | | | | Consider a monic polynomial with integer coefficients: $latex p(x)=x^d + a_1 x^{d-1} + \cdots + a_{d-1}x + a_d$, $latex a_j \in \mathbb{Z}$.The complex roots of such polynomials are called algebraic integers. For example, integers and the roots of integers are algebraic integers. Note that the Galois conjugates of an algebraic integer are also algebraic integers.... | |
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mathematicaloddsandends.wordpress.com
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| | | | | I recently came across this theorem on John Cook's blog that I wanted to keep for myself for future reference: Theorem. Let $latex f$ be a function so that $latex f^{(n+1)}$ is continuous on $latex [a,b]$ and satisfies $latex |f^{(n+1)}(x)| \leq M$. Let $latex p$ be a polynomial of degree $latex \leq n$ that interpolates... | |
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algorithmsoup.wordpress.com
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| | | | | The ``probabilistic method'' is the art of applying probabilistic thinking to non-probabilistic problems. Applications of the probabilistic method often feel like magic. Here is my favorite example: Theorem (Erdös, 1965). Call a set $latex {X}&fg=000000$ sum-free if for all $latex {a, b \in X}&fg=000000$, we have $latex {a + b \not\in X}&fg=000000$. For any finite... | |
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soatok.blog
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| | | Recently, it occurred to me that there wasn't a good, focused resource that covers commitments in the context of asymmetric cryptography. I had covered confused deputy attacks in my very short (don't look at the scroll bar) blog post on database cryptography., and that's definitely relevant. I had also touched on the subject of commitment... | ||
