IMO 1976 LL GDR21

Find the largest positive real number p (if it exists) such that

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IMO 1976 LL GDR21

Origin: GDR

Problem

Find the largest positive real number p (if it exists) such that the inequality x2 1 + x2 2 + \cdot \cdot \cdot + x2 n \geqp(x1x2 + x2x3 + \cdot \cdot \cdot + xn−1xn) (1) is satisfied for all real numbers xi, and (a) n = 2; (b) n = 5. Find the largest positive real number p (if it exists) such that the inequal- ity (1) holds for all real numbers xi and all natural numbers n, n \geq2.