On fourth degree equations

Some Fourth Degree Diophantine Equations in Gaussian Integers

For certain choices of the coefficients a, b, c the solutions of the Diophantine equation ax+by = cz in Gaussian integers satisfy xy = 0.

Fourth Order Equations In

Immediate haemorrhoidectomy for thrombosed fourth degree haemorrhoids.

Madam, We mad with interest a short report published in your November issue titled "Immediate Haemorrhoidectomy for Thrombosed Fourth Degree Haemorrhoids”. The Author has compared the results of immediate haemorrhoidectomy and conservative treatment. Unfortunately, be did not mention the treatment that we have found simple and effective in thrombosed, prolapsed haemorrholds. Head and Gudgeon re...

Ratio vectors of fourth degree polynomials

Let p(x) be a polynomial of degree 4 with four distinct real roots r1 < r2 < r3 < r4. Let x1 < x2 < x3 be the critical points of p, and define the ratios σk = xk − rk rk+1 − rk , k = 1, 2, 3. For notational convenience, let σ1 = u, σ2 = v, and σ3 = w. (u, v, w) is called the ratio vector of p. We prove necessary and sufficient conditions for (u, v, w) to be a ratio vector of a polynomial of deg...

ON EQUATIONS OF THE FIFTH DEGREE By