IMO 1983 LL ROM56

Origin: ROM

Problem

Consider the expansion (1 + x + x2 + x3 + x4)496 = a0 + a1x + \cdot \cdot \cdot + a1984x1984. (a) Determine the greatest common divisor of the coefficients a3, a8, a13, . . . , a1983. (b) Prove that 10340 < a992 < 10347.