Raghavendra (2012) A Randomized Algorithm for Linear Equations over Prime Fields
Summary at: [1] http://rjlipton.wordpress.com/2012/08/09/a-new-way-to-solve-linear-equations/
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Proof of Euclid's Formula for Pythagorean Triples
Euclid’s formula says that, \((a,b,c)\) are a Pythagorean triple, i.e.,
\(a^2+b^2=c^2\) for \(a,b,c\) are integers, if and only if \(a=2mn\), \(b=m^2-n^2\),
\(c=m^2+n^2\) for some integers \(m,n\).
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Revision: Ito calculus
Stochastic process: \(X(t), t\in[0,\infty)\)
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Integer Reciprocal and Geometric Series
Note that
\(\frac{1}{3} = \frac{1}{4} + \frac{1}{16} + \frac{1}{64} + \frac{1}{256} + \cdots\)
In fact, we have
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Opposite of a Bloom Filter
Bloom filter gives a \(O(1)\)-efficient way to test for set memberships, but with false positives and no false negatives, i.e. it will tell you \(x\in S\) while actually it is not, but not vice versa.
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