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awwalker.com | ||
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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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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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mattbaker.blog
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| | | | | In this post, I'd like to explain a proof of the Law of Quadratic Reciprocity based on properties of Lucas polynomials. (There are over 300 known proofs of the Law of Quadratic Reciprocity in the literature, but to the best of my knowledge this one is new!) In order to keep this post as self-contained... | |
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ropmann.wordpress.com
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