IMO 1976 Shortlist

IMO 1976 Shortlist — 12 problems. 12 problems.

12 items

IMO 1976 Shortlist

12 problems · Source: IMO Compendium

Problems

# Origin Problem
1 BUL Let ABC be a triangle with bisectors AA1, BB1, CC1 (A1 \in
2 BUL Let a0, a1, . . . , an, an+1 be a sequence of real numbers satisfying
3 CZS In a convex quadrangle with area 32 cm2, the sum of the
4 (GBR 1a)IMO6 For all positive integral n, un+1 = un(u2
5 NET Let a set of p equations be given,
6 NET A rectangular box can be filled completely with unit cubes.
7 (POL 1b) Let I = (0, 1] be the unit interval of the real line. For a given
8 SWE Let P be a polynomial with real coefficients such that P(x) > 0
9 FIN Let P1(x) = x2 −2, Pj(x) = P1(Pj−1(x)), j = 2, 3, . . . .
10 USA Find the largest number obtainable as the product of pos-
11 VIE Prove that there exist infinitely many positive integers n such
12 VIE The polynomial 1976(x+x2+\cdot \cdot \cdot+xn) is decomposed into a sum