MathDB
M 27

Source:

May 25, 2007
modular arithmeticcalculusinductionvectorabstract algebraalgebrapolynomial

Problem Statement

Let p≥3 p \ge 3 be a prime number. The sequence {an}n≥0 \{a_{n}\}_{n \ge 0} is defined by an=n a_{n}=n for all 0≤n≤p−1 0 \le n \le p-1, and an=an−1+an−p a_{n}=a_{n-1}+a_{n-p} for all n≥p n \ge p. Compute ap3  (modp) a_{p^{3}}\; \pmod{p}.
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