Question

Prove that there are no positive perfect cubes less than 1000 that are the sum of the
cubes of two positive integers.

Answer 1

Answer:

The only positive integer cubes below 100 are 1 , 8 , 27 and 64

Nothing further.

Method 1: Add them

1+8+27+64

=9+91=100

Method 2: Be a smarty-pants and use the formula (absolutely unnecessary to do it this way)

Sn=n2(n+1)24

where Sn is the number of positive integer cubes considered.

We also get Sn=100 .

Step-by-step explanation:

And there are only 9 perfect cubes.