# Indeterminate equation sentence example

A few problems lead to indeterminate equations of the third and fourth degrees, an easy

**indeterminate equation**of the sixth degree being also found.The Diophantine analysis was a favourite subject with Pell; he lectured on it at Amsterdam; and he is now best remembered for the

**indeterminate equation**ax 2 +1 = y 2, which is known by his name.The solution in integers of the

**indeterminate equation**ax+by=c may be effected by means of continued fractions.In the case of a recurring continued fraction which represents N, where N is an integer, if n is the number of partial quotients in the recurring cycle, and pnr/gnr the nr th convergent, then p 2 nr - Ng2nr = (- I) nr, whence, if n is odd, integral solutions of the

**indeterminate equation**x 2 - Ny 2 = I (the so-called Pellian equation) can be found.Advertisement