2 May
2003
2 May
'03
8:13 a.m.
When I solved [1] 8 x^2 - 343 y^2 = 1, all solutions (x, y) were of the form (26041 j, 3397 k). An similar situation appears to be true of 22 x^2 - 29 y^2 = 1, where all solutions (x, y) seem to be of the form (31 j, 27 k). For which (a, b) do all solutions of a x^2 - b y^2 = 0 have the form (r k, s j) for some fixed r, s > 1?