MathDB

Ms. Math's kindergarten class has

16

registered students. The classroom has a very large number,

N

, of play blocks which satisfies the conditions:
(a) If

16

15

, or

14

students are present, then in each case all the blocks can be distributed in equal numbers to each student, and (b) There are three integers

0 < x < y < z < 14

such that when

x

y

, or

z

students are present and the blocks are distributed in equal numbers to each student, there are exactly three blocks left over.
Find the sum of the distinct prime divisors of the least possible value of

N

satisfying the above conditions.

Problem Statement