# Tagged Questions

I have a question on my mind I am trying to solve. However I am stuck at a point. If you could help, I would be very pleased. $$\frac {x_2y_2z_2}{x_2y_2+y_2z_2+x_2z_2}=\frac ... 0answers 99 views ### Quadratic Diophantine Equations in Polynomial Time Considering the problem of finding lattice points (x_1, x_2 ... x_n) that satisfy a quadratic law: F(x_1, x_2... x_n) = 0 such that F(x_1, x_2... x_n) is a second degree polynomial It is ... 3answers 261 views ### Way to show x^n + y^n = z^n factorises as (x + y)(x + \zeta y) \cdots (x + \zeta^{n-1}y) = z^n For odd n the Fermat equation x^n + y^n = z^n factorises as$$(x + y)(x + \zeta y) \cdots (x + \zeta^{n-1}y) = z^n,$$where \zeta = e^{2 \pi i/n}. I tried seeing this was true by multiplying ... 2answers 184 views ### Are Euclid numbers squarefree? Are Euclid numbers squarefree ? An Euclid number is by definition a Primorial number + 1. See http://mathworld.wolfram.com/Primorial.html. In notation the n th Euclid number is written as E_n = ... 1answer 238 views ### Factoring a trivariate polynomial I would appreciate some help with factoring a trivariate polynomial. The polynomial in question is$$p(x,y,z)=a_1 x^7+a_2 x^5y+a_3 x^3y^2+a_4 xy^3+a_5 x^4z+a_6 x^2yz+a_7 y^2z+a_8 xz^2, where the ...
This is in relation to a problem dealing with the three-dimensional analogue of Pell's Equation. I would like to factor $x^3+Dy^3+D^2z^3-3Dxyz$ into $\frac{1}{2}(x+Dy+D^2y)$ and another factor. I ...