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3 primes (Posted on 2015-06-22) Difficulty: 1 of 5
Define all triplets (x, y, z) such that x, y, z, x-y, y-z, x-z
are all positive primes.

No Solution Yet Submitted by Ady TZIDON    
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Solution Analytical Solution Comment 2 of 2 |
x and y must be greater than 2, and both odd, so their difference must be two.

If z = 2, then y-2 and y and x are all prime.
The only prime triplet is 3,5,7, so x = 7 and y = 5

What if z is not 2?
Then x, y and z are all odd.
Then x - y = 2 and y - z = 2, so x - z = 4, which is not prime.

So there is only 1 solution.

  Posted by Steve Herman on 2015-06-22 12:44:14
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