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