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Diophantine And Almost Fermat (Posted on 2007-02-21) Difficulty: 3 of 5
Consider three positive integers x< y< z in arithmetic sequence.

Determine analytically all possible solutions of each of the following equations:

(I) x3 + z3 = y3 + 10yz

(II) x3 + y3 = z3 - 2, with y< 116.

See The Solution Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

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Hints/Tips Hint | Comment 1 of 4

Since x<y<z are three positive integers  in arithmetic sequence (for both the parts I and II) , one may substitute:
x = y-a and z = y+a where a is a positive integer.................

: Remember that each of x, y and z must be positive integers for both the parts.

Edited on February 22, 2007, 1:52 pm

Edited on February 22, 2007, 1:53 pm

Edited on February 22, 2007, 2:05 pm
  Posted by K Sengupta on 2007-02-22 13:51:46

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