Find the missing Ramanujan number for the following: $2^{3} + 24^{3} =$ __ $+ 20^{3} .$

2^{3} + 24^{3} = 18^{3} + 20^{3}

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2^{3} + 24^{3} = 16^{3} + 20^{3}

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2^{3} + 24^{3} = 14^{3} + 20^{3}

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2^{3} + 24^{3} = 12^{3} + 20^{3}

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Solution

The correct option is D $2^{3} + 24^{3} = 18^{3} + 20^{3}$
Ramanujan number expressible as the sum of two cubes in two different ways.
So,
$2^{3} + 24^{3} = 18^{3} + 20^{3}$
$8 + 13824 = 5832 + 8000$
$13832 = 13832$
So, the missing number is $18^{3} .$

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