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Determine the greatest common divisor of the coefficients

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October 7, 2010
symmetrynumber theorygreatest common divisorfunctionnumber theory unsolved

Problem Statement

Consider the expansion (1+x+x2+x3+x4)496=a0+a1x+⋯+a1984x1984.(1 + x + x^2 + x^3 + x^4)^{496} = a_0 + a_1x + \cdots + a_{1984}x^{1984}. (a) Determine the greatest common divisor of the coefficients a3,a8,a13,…,a1983.a_3, a_8, a_{13}, \ldots , a_{1983}.
(b) Prove that 10340<a992<10347.10^{340 }< a_{992} < 10^{347}.
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