Consider three positive integers x < y < z in arithmetic sequence, and determine all possible solutions of:
x4 + y4 = z4 - 64
A computer program finds
1,2,3 and 7,8,9 as the only sets of values for x,y and z up to a y value of over 11,000, as
FOR t = 2 TO 1000000
FOR x = 1 TO t - 1
incr = t - x
y = x + incr: z = y + incr
IF x * x * x * x + y * y * y * y = z * z * z * z - 64 THEN
PRINT x, y, z
END IF
NEXT
NEXT
was stopped with t above 11,000 (y is the same as t).
|
|
Posted by Charlie
on 2006-06-27 16:02:16 |
not a proof but may be spoiler
