# Indeterminate equation sentence example

indeterminate equation

- 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.
- For proofs of the theorems here stated and for applications to the more general indeterminate equation x 2 - Ny 2 = H the reader may consult Chrystal's Algebra or Serret's Cours d'Algbbre Superieure; he may also profitably consult a tract by T.Advertisement