Diofrantic

From: Ian Hutcheson (Ian_at_z9y8.fsnet.co.uk)
Date: 01/22/05 

Date: Sat, 22 Jan 2005 11:35:19 -0000

I am new at this subject and would be interested to know a
method, of obtaining integer
solutions to

a^3 + b^3 = 22*c^3

This is not homework; I came across the problem in a popular
maths book and realised I do not know how to approach the
problem apart
from the trial and error methods.

Tried a^3 + b^3 = (a +b)(a^2-ab +b^2) and experimented with

(a +b) = 22 leading to search for integer values of c =
(3a^2 -66a +484)^(1/3)

Graphing only indicated c>5, and not easy to see integer a
and c from this.

Experimenting with (a^2-ab +b^2) = 22 did not deliver
integer values either.

Would appreciate if someone could completely lay out the
proper way of
doing this.

Regards - Ian Hutcheson

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