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        riddles >> medium >> sum of distinct cubes
        
(Message started by: Christine on Aug 14^th, 2014, 9:42am)

Title: sum of distinct cubes
Post by Christine on Aug 14^th, 2014, 9:42am

Cubes with a representation as a sum of distinct cubes :

Some end with a 1^3 : 9^3 = 8^3 + 6^3 + 1^3

others don't : 6^3 = 5^3 + 4^3 + 3^3

Is the set of those that don't finite or infinite?

How to prove it?

Title: Re: sum of distinct cubes
Post by towr on Aug 14^th, 2014, 10:08am

[hide]multiply by n^3
if a^3 = b^3 + c^3 + d^3 then (an)^3 = (bn)^3 + (cn)^3 + (dn)^3[/hide]