Let k be a prime integer such that \(\displaystyle 100 < k < 225\). How many distinct values of k exist such that \(\displaystyle k = a^{3} + b^{3}\) where a and b are both positive integers?

The answer key says 0 and I suspect this has something to do with k being prime. What's the explanation behind this?

The answer key says 0 and I suspect this has something to do with k being prime. What's the explanation behind this?

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