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values of term in sequence

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October 14, 2009
number theory unsolvednumber theory

Problem Statement

Let n>1 n>1 and for 1≤k≤n 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 a1,a2,...,an a_1,a_2,...,a_n. Furthermore let P \equal{} P(a_1, a_2, . . . , a_n) be the sum of all pk p_k with odd values of k k less than or equal to n n. How many different values are taken by aj a_j if all the numbers aj(1≤j≤n) a_j (1 \leq j \leq n) and P P are prime?
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