We are in the right year for this! - (4)

Number Theory Level 3

First: Find all distinct triples $(x_1,y_1,z_1), (x_2,y_2,z_2), \dots$ that suffice the following properties:

$x*(y+z) = 2015$ ,

$y > z$ ,

$x,y,z$ are primes!

Then: What is the sum of: $x_1 + x_2 + \dots + y_1 + y_2 \dots + z_1 + z_2 + \dots$

1 solution

Karen Black
Oct 13, 2015

Factor 2015 to find possible x: 5, 13 & 31.

For x=5, y+z=403, and remembering that "even plus odd equals odd" means that z=2 (only even prime). Thus for this set, y=401 and is prime.

For x=13, y+z=155; since z still has to be 2, y=153. But this y is not prime, so the triple is thrown out.

For x=31, y+z=65; z=2, y=63 and again y is not prime and the triple is thrown out.