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Further Arithmetic Integers (Posted on 2006-06-27) Difficulty: 3 of 5
Consider three positive integers x < y < z in arithmetic sequence, and determine all possible solutions of: x4 + y4 = z4 - 64

See The Solution Submitted by K Sengupta    
Rating: 2.5000 (2 votes)

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Hints/Tips not a proof but may be spoiler | Comment 1 of 10

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
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