P131
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Prime Cube Partnership

ℹ️Published on Friday, 10th November 2006, 06:00 pm; Solved by 8248;
Difficulty rating: 40%

There are some prime values, p, for which there exists a positive integer, n, such that the expression n3+n2p is a perfect cube.

For example, when p=19, 83+82×19=123.

What is perhaps most surprising is that for each prime with this property the value of n is unique, and there are only four such primes below one-hundred.

How many primes below one million have this remarkable property?



Soluzione

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