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2\times 3\times 5\times 11
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Algebra
5 problemes similars a:
factor(330)
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Note that the period for a prime p is a factor of \varphi (p)=p-1 but need not be equal to it. This is because 10^{p-1} \equiv 1 \mod p. The period is the least n for which p|(10^n-1). If ...
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This question reminded me of several notes by the influential computer scientist Edsger W. Dijkstra, who spent a lot of time thinking about how our notation can affect how we think and reason ...
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Suppose m,n > N. Then f_m(x) = f_n(x) = -1 when x \in [0, \frac{1}{2}-\frac{1}{N}]. Similarly, f_m(x) = f_n(x) = +1 when x \in [\frac{1}{2}+\frac{1}{N},1]. And |f_m(x)-f_n(x)| \leq 1 ...
Cayley-Hamilton Theorem proof
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You are trying to show that: (P^{-1}AP-\lambda_{1}I)^{k_{1}}\dots(P^{-1}AP-\lambda_{m}I)^{k_{m}}=0 let's take one subspace: (P^{-1}AP-\lambda_{1}I)^{k_{1}} then it's equal to \begin{bmatrix} ...
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