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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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re(2): Solution | Comment 9 of 10 |
(In reply to re: Solution by Yosippavar)


For example the equation for y = 8:
    65 = k*(k^2+64)
k must be a factor of 65
    k   k^2+64   k*(k^2+64)
  --------------------------
    1      65          65
    5      89         445
   13     233        3029
   65    4289      278785
So you see that k = 1 is only valid factor.

 

  Posted by Bractals on 2006-06-28 10:53:32
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