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.

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.................

Important: 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