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Jul
29
comment How to solve this system for real $x,y,z$
@bub, first of all, I decided to look for positive integer solutions. There may be lots of other solutions, but I'll let someone else find them. Then from (1), $z\le2$; from (2), $x\le4$; from (3), $y\le3$. So there is nothing more natural than to see whether $(4,3,2)$ works. It does.
Jul
29
comment How to solve this system for real $x,y,z$
$(x,y,z)=(4,3,2)$.
Jul
28
comment matrix representation of polynomial
Any polynomial $\sum c_{ij}x_ix_j$ of degree 2 is $v^tAv$ for $v=(x_1,\dots,x_n)$, and entry $a_{ij}$ of $A$ given by $(c_{ij}+c_{ji})/2$.
Jul
28
comment The characteristic function of primes and the omega function
Do you know what the mobius transform is? Do you know about Mobius inversion?
Jul
27
revised Is every holomorphic function in a neighborhood of the origin of $C^n$ necessarily bounded?
more informative title
Jul
27
comment Is it possible to get logical and with linear operations?
This would seem to be a problem about programming. There's a website for coding questions.
Jul
27
comment the strategy about a $0-1$ matrix game
Is this a one-person game? where you can make any move you like? and as many moves as you like? If it is, just change each 1 to a 0, one at a time.
Jul
27
comment What should be the method for solving and solution of $\frac{x^2+y^2}{x^2-y^2}$?
Let $u=x/y$, rewrite everything in terms of $u$, and solve.
Jul
26
answered Is $\tan (\pi x)$ never rational for all rational $x$ in the interval $(-0.5,0.5)$, with the exceptions occuring at $x=0, -0.25, 0.25$?
Jul
26
comment Is $\tan (\pi x)$ never rational for all rational $x$ in the interval $(-0.5,0.5)$, with the exceptions occuring at $x=0, -0.25, 0.25$?
It is well-known exactly which rational $x$ result in rational values of $\tan\pi x$, $\sin\pi x$, and so on. You can probably find the details in Niven's book on irrational numbers.
Jul
26
comment How to solve this second order DE question?
Nice, but can you edit that last display so as to make the exponent visible without a microscope?
Jul
26
comment Find the sum of series $\sum_{n=0}^\infty\frac{(4n)!}{(4n+4)!}$
@lab, numerator is zero-factorial, seems right to me.
Jul
26
answered Prime patterns in different form representation need attention
Jul
26
comment Measurements on a unit circle
It would be nice of you to provide some context, for example, where does the problem come from, why do you want an answer, what progress have you made, where are you getting stuck, that sort of thing.
Jul
26
comment How to solve this second order DE question?
That power on the $y'$ is what makes it nonlinear and blows your assumed solution out of the water.
Jul
26
comment How to solve this second order DE question?
It's not homogeneous --- not with that $r$ in it.
Jul
26
answered How to calculate weight of positive and negative values.
Jul
26
comment How to solve this second order DE question?
Numerically. Second-order nonlinear differential equations generally don't have closed form solutions. Do you have some reason to think this one does?
Jul
26
comment Is a Bijection From a Group to Itself Automatically an Isomorphism If It Maps the Identity to Itself?
Try some other group.
Jul
26
comment Analytical expression for the height of a circular segment
Numerically is the only way to go on that one.