2016 · Q22
Which one of the following is correct in respect of the number 1729 ?
Elementary MathematicsNumber System
- AIt cannot be written as the sum of the cubes of two positive integers
- BIt can be written as the sum of the cubes of two positive integers in one way only
- CIt can be written as the sum of the cubes of two positive integers in two ways only
- DIt can be written as the sum of the cubes of two positive integers in three ways only
Explanation
1729 = 12³+1³ = 1728+1, and also 1729 = 10³+9³ = 1000+729 — the famous Hardy–Ramanujan number. It is expressible as a sum of two positive cubes in exactly two ways (option C).