MathDB

Let

n>1

and for

1 \leq k \leq n

let p_k \equal{} p_k(a_1, a_2, . . . , a_n) be the sum of the products of all possible combinations of k of the numbers

a_1,a_2,...,a_n

. Furthermore let P \equal{} P(a_1, a_2, . . . , a_n) be the sum of all

p_k

with odd values of

k

less than or equal to

n

. How many different values are taken by

a_j

if all the numbers

a_j (1 \leq j \leq n)

and

P

are prime?

5