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how do we prove that if $a^2+b^2=c^2$, and they are all integers, there would be at least one of them to a multiple of 5.What I did is...
Asked on 12/02/2020 by Henry Cai
1 answerLet $V$ be an inner product space with a basis $(v_1,...,v_n)$. I know that the Gram matrixbegin{equation}G=begin{pmatrix}langle v_1,v_1rangle&cdots&langle v_1,v_nrangle\vdots&&vdots\langle v_n,v_1rangle&cdots&langle v_n,v_nrangleend{pmatrix}=begin{pmatrix}...
Asked on 12/01/2020 by Filippo
2 answerA bus goes to $3$ bus stops, at each stop $3/4$ of the people on the bus get off and $10$ get on. what is the minimum...
Asked on 12/01/2020 by Mathie102
4 answerI have an PDE $dfrac{df}{d xi}-xidfrac{d x_1}{d xi}=0$ homogeneous for $xi$, where $f:mathbb{R}^ntomathbb{R}$ is function of $x_1,cdots,x_n:mathbb{R}tomathbb{R}$, which in turn are functions of $xi$ (so,...
Asked on 12/01/2020 by Still_waters
1 answerFor the given parameter $mathbb Rni tgeq 1$, the sequence is defined recursively: $$a_1=t,;;a_{n+1}a_n=3a_n-2$$ $(a)$ Let $t=4$. Prove the sequence $(a_n)$...
Asked on 12/01/2020 by Invisible
2 answer$mathrm{Vect}_k(M)$ is the isomorphism classes of real $k$ rank vector bundles over $M$.In Bott-Tu book they give only an example:For contractible manifolds it is ...
Asked on 12/01/2020 by KoKo
0 answerGiven $$(I+T_1T_2T_3),x = b$$ where $I$ is the identity matrix and $T_1$, $T_2$ and $T_3$ are invertible upper triangular matrices. Matrix $(I+T_1T_2T_3)$ is also invertible. I want to know what...
Asked on 12/01/2020 by J.Ricky
2 answerHow many people are needed to guarantee that at least two were born on the same day of the week and in the same month (perhaps in different years) ?...
Asked on 11/30/2020 by Keshav Vinayak Jha
2 answerReading the wikipedia page for "Topological Space", three axiomatizations are presented for defining topological spaces. They are presented as equivalent. The first is attributed to Hausdorff and uses neighbourhoods, the...
Asked on 11/30/2020 by Christine
2 answerThis cropped up in an otherwise simple-looking problem. Find the solutions for $a, b, n in mathbb{Z}$ and $b, n > 1$ for the Diophantine equation: $b^n...
Asked on 11/30/2020 by highgardener
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