Analytically determine all possible solutions of the equation :
[p/2]² + [p/3] = 498, whenever p is a positive integer.

Note: [x] is defined as the greatest integer less than or equal to x.

Correction to explanation (sorry...):

Which yields only x=22, and therefore y=14 (since y=498-x^2).
This means that:
p in [2x, 2x+2)
p in [44, 46)
p is 44 or 45
...AND...
p in [3y, 3y+3)
p in [42, 45)
p is 42, 43 or 44

Only p=44 satisfies both conditions.

Posted by Kurious on 2007-04-16 11:27:57