Recent content by DianaSagita

Homework Statement If all vertices of planar graph have degrees greater than 4, prove if that graph has at least 12 vertices with degree of 5. Homework Equations d1+d2+...+dn= 2*m (m - number of edges, di-degree of i-vertex) f=2-n+m, f - number of faces, n-number of vertices The...

Thank you, rasmhop! I understand now how to get it, your reply was helpful, cheers!

Homework Statement Prove if there exists an integer whose decimal notation contains only 0s and 1s, and which is divisible by 2009. Homework Equations Dirichlet's box principle :confused: The Attempt at a Solution I'm new to number theory, and I'm aware that I do not have the...

Well, thanks a lot, it seems correct! Meanwhile, I did it too... According to Euler's Theorem: 5^{p^{2}-p}\equiv 1(mod\ p^{2}) 5^{p^{2}}\equiv 5^{p}(mod\ p^{2}) 5^{p^{2}}-5^{p}\equiv 0(mod\ p^{2}) 5^{p^{2}}+1-(5^{p}+1)\equiv 0(mod\ p^{2}) So, if 5^{p^{2}}+1 is divisible by p2, then...

Homework Statement First of all, hi everyone! I'm quite new in number theory, and need help on this one badly... Determine all prime numbers p so p2 divides 5p2+1. Homework Equations Euler's theorem: If a and m are coprimes then...

I've got it! f(z)=e^{D_1(x)+D_{1num}-\frac{y^2}{2}+ixy} f(z)=e^{D_2(y)+D_{2num}+\frac{x^2}{2}+ixy} so... D_1(x)+D_{1num}-\frac{y^2}{2}=D_2(y)+D_{2num}+\frac{x^2}{2} D_1(x)=\frac{x^2}{2} D_2(y)=-\frac{y^2}{2} D_{1num}=D_{2num}=D and analytical function is...

Thanks, and that's what I did... now I got... u=e^{-{\frac{y^2}{2}}}cos(xy)C_1 solving by u_y^' u=e^{\frac{x^2}{2}}cos(xy)C_2 solving by u_x^' C_1,C_2 constants C_1=e^{D_1},C_2=e^{D_2} so I have functions... f(z)=e^{D_1-\frac{y^2}{2}+ixy} f(z)=e^{D_2+\frac{x^2}{2}+ixy} How two...

Well, I must find modulo... and this one you entered is not analytical function... :(

1. This is something from complex analysis: Find the analytic function f(z)= f(x+iy) such that arg f(z)= xy. 2. w=f(z)=f(x+iy)=u(x,y)+iv(x,y) (*), w=\rho e^{i\theta} (**) Here are the Cauchy-Riemann conditions... \frac{\partial u}{\partial x}=\frac{\partial v}{\partial...

Thanks a lot. I did it! :)

Volume Integral! Help! I need help with this: Find volume of figure bounded with surface (x^2+y^2+z^2+1)^2=8*(x^2+y^2) I tried Ostrogradsky, and spherical coordinate system with it, but I can't find boundaries... PLEASE! HELP ME!