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 Algebra and Primes (Posted on 2013-12-25)
Find all triples (x, y, z) of positive integers such that x³ + y³ + z³ - 3xyz = p

where p is a prime greater than 3

 No Solution Yet Submitted by Danish Ahmed Khan Rating: 4.0000 (3 votes)

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 PARITY et all Comment 3 of 3 |
Upon parity considerations, it was clear to me that the triplet must contain two even and one odd integer, otherwise p=even.

Although I have found few sample triplets, I did not perceive
that there are two equal integers and one odd  neighbor.

After seeing Ch's output I realized that  the sums cover all prime numbers.

Enter SH, -  Saying - "give me a prime (over 3) and I will give you a triplet" 17=>6,6,5,  19=>6,6,7,  101=>34,34,33  etc

Nice puzzle - I have rated it 4.

 Posted by Ady TZIDON on 2013-12-25 14:40:51

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