PELL'S EQUATION

By KAREN ANDERSON

CONTENTS 1 THE SQUARE ROOT OF 2 PROBLEMS LEADING TO PELL’S EQUATION AND PRELIMINARY INVESTIGATIONS 3 QUADRATIC SURDS 4 THE FUNDAMENTAL SOLUTION 5 TRACKING DOWN THE FUNDAMENTAL SOLUTION 6 PELL’S EQUATION AND PYTHAGOREAN TRIPLES 7 THE CUBIC ANALOGUE OF PELL’S EQUATION 8 ANALOGUES OF THE FOURTH AND HIGHER DEGREES 9 A FINITE VERSION OF PELL’S EQUATION