[net.math] Pell's

kp@smu.UUCP (04/20/84)

#N:smu:14100002:000:321
smu!kp    Apr 20 15:39:00 1984


   Consider equations of following type:

             x^2 - d*y^2 = 1   where x, y, d are all positive integers.

  Can you give me the least positive integral solutions in x and y,  
if they exist, for the following equations:

    (1)  X^2 - 961*Y^2 = 1

    (2)  X^2 - 991*Y^2 = 1

             ( Answer next week )

gmf@uvacs.UUCP (04/23/84)

I know the solution to  x^2 - 961*y^2 = 1 .  It is given on p. 88 of
Sierpinski's  *Elementary Theory of Numbers* .  I also know the
solution to  x^2 - 991*y^2 = 1.  It is given on p. 93.  Sierpinski
remarks that the solution to one of these illustrates a peril of
induction.  Additional question:  What peril?

     Gordon Fisher