Solving binary quadratic Diophantine equations A remarkably direct approach allows one to generally solve binary quadratic Diophantine equations. Given an equation of the form c1x2 + c2xy + c3y2 = c4 + c5x + c6y I've proven that (2A(x+y) - B)2 - 4As2 = B2 - 4AC ...Considering a Diophantine chain I am curious about the latest result and figured a simple test would allow me to see what Diophantine chains look like, so here goes. The method works with an equation of the form c1x2 + c2xy + c3y2 = c4 + c5x + c6y ... IIT Maths Sample Paper 1- Algebra 1. Let x be a real number with 0 2. Use combinatorial argument to prove the identity: ?? ?? n-r+1 C d . r-1 C d-1 = n C r d=1 3. a , b are roots of x 2 +ax+b=0, g , d are roots of x 2 -ax+b-2=0. Given 1/ a + 1/ b + 1/ d + 1/ g =5/12 and ... Quadratic Diophantine Result Quadratic Diophantine Theorem: In the ring of integers, given the quadratic expression c1x2 + c2xy + c3y2 = c4z2 + c5zx + c6zy where the c's are constants, for solutions to exist it must be true that ((c2 - 2c1)2 + 4c1(c2 - c1 - c3))v2 ... Quadratic Diophantine Theorem and Pell's Equation With the Quadratic Diophantine Theorem derived, it makes sense to try it out with a well-known equation in Diophantine theory which is Pell's Equation: x2 - Dy2 = 1 with D a natural number. Now again, the Quadratic Diophantine Theorem: ... Re: solve system of equations leo nidas wrote: > I am trying to estimate the parameters of the generalized gamma distribution with > the method of moments. Just wanted to solve the system of equation and since matlab > doesn't have any function of producing random ... Rapid Share accounts i am noticing a lot of posts link to rapid share. does anyone know where i can get a cheap rapid share account from ? thanks. Solvability and Diophantine Quadratic Chains Deciding to take my newly discovered Quadratic Diophantine Theorem for a spin against "Pell's Equation" turned out to be a good idea as besides letting me validate that I had derived the theorem correctly, it also showed me that the ... |