Fibonacci and Matijasevic

摘要

In 1900,at the Second International Congress of Mathematicians in Paris, David Hilbert, one of the leading mathematicians of the time, posed his now-famous 23 problems. The tenth of these seeks a 'process' involving a finite number of operations to determine whether any given Diophantine equation D(xi,…,x_m) = 0 has a solution in integers xi,...,x_m where D is a polynomial with integer coefficients. These equations are named after the Greek mathematician Diophantus who lived in the third century AD and was interested in problems of this kind.