The Equation f(X) = f(Y) in Rational Functions X = X(t), Y = Y(t)

Prove : ∀ x Fx Solve : ∃ x Fx Compute : λx Fx 3

ON THE DIOPHANTINE EQUATION x + y = 2pz

We show, if p is prime, that the equation xn + yn = 2pz2 has no solutions in coprime integers x and y with |xy| ≥ 1 and n > p132p , and, if p 6= 7, the equation xn + yn = pz2 has no solutions in coprime integers x and y with |xy| ≥ 1 and n > p12p .

A probabilistic view on possibility distributions

In this work we shall give a probabilistic interpretation of possibilistic expected value, variance, covariance and correlation. 1 Probability and possibility In probability theory, the dependency between two random variables can be characterized through their joint probability density function. Namely, if X and Y are two random variables with probability density functions fX(x) and fY (y), res...

The Diophantine equation f(x) = g(y)

have finitely or infinitely many solutions in rational integers x and y? Due to the classical theorem of Siegel (see Theorem 10.1 below), the finiteness problem for (1), and even for a more general equation F (x, y) = 0 with F (x, y) ∈ Z[x, y], is decidable (). One has to: • decompose the polynomial F (x, y) into Q-irreducible factors; • for those factors which are not Q-reducible, determine th...

Rational Distance Sets on X Y = 1

We consider the problem of finding sets of points on xy = 1, where all of the interpoint distances are rational. The search for such points has links to both congruent and concordant numbers.