Determine the integer(s) n for which [n²/3] is a prime.
Note: [x] is the greatest integer ≤ x (floor function).

The integers are 3 and 4. Three cases:

n=3a:
[n^2/3]=3a^2 => a=1 and n=3

n=3a+1:
[n^2/3]=a(3a+2) =>a=1 and n=4

n=3a+2:
[n^2/3]=(a+1)(3a+1) => No solution

Posted by JLo on 2006-12-09 11:18:49