Consider three positive integers x< y< z in arithmetic sequence.

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

(I) x^{3} + z^{3} = y^{3} + 10yz

(II) x^{3} + y^{3} = z^{3} - 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**