Posted by anonymous on Tuesday, July 2, 2013 at 12:58pm.
What is the largest integer less than 1000 that can be represented as a^3+b^3+c^3 for some integers a,b,c, such that a+b+c=0.

math  MathMate, Tuesday, July 2, 2013 at 4:39pm
By trial and error, I get:
11^3+(5)^3+(6)^3=990
If we assume the largest integer is N such that
N(a,b)=a^3b^3(ab)^3
=3ab(ab)
The likely candidates are:
990=3*11*5(115)... a,b,c = 11, 5, 6
993=3*331
996=3*332=3(4*83)
999=3*333=3(9*37)
All of which cannot be reduced to the form
3ab(ab).
Answer This Question
Related Questions
 la sallle  There are 3 consecutive even integers such that the quotient ...
 calculus  A positive multiple of 11 is good if it does not contain any even ...
 heeeeeeeeelp math  For every positive integer n consider all polynomials f(x) ...
 heeeeeelp math  For every positive integer n, consider all polynomials f(x) ...
 Math  Find three consecutive even integers such that the sum of the smallest ...
 heeeeeeelp math  For every positive integer n, consider all monic polynomials f...
 Math (algebra)  For every positive integer n, consider all monic polynomials f(...
 math  What is the smallest of three consecutive integers if the sum of the ...
 math  What is the smallest of three consecutive integers if the sum of the ...
 heeeeeeelp math3  For every positive integer n consider all polynomials f(x) ...
More Related Questions