(a) Show that 39312 = 2^3 + 34^3 = 15^3 + 33^3. (b) Using prime factorisation, show that 39312 itself is not a perfect cube.

Question

TextHardy-Ramanujan NumbersCube Root by Prime Factorisation Method

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The smallest number by which 392 must be multiplied to get a perfect cube is

The smallest number by which 1323 must be divided so that the quotient is a perfect cube is

Properties of Cube Numbers

Cube Root by Prime Factorisation Method

The value of \sqrt[3]{-3375} is

The value of \sqrt[3]{\dfrac{27}{343}} is

The smallest number that can be written as the sum of two cubes in two different ways is

Which pair of cubes gives 1729 in the second way (other than 1^3 + 12^3)?