MathDB

27

Part of PEN M Problems

Problems(1)

M 27

Source:

5/25/2007
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}.
modular arithmeticcalculusinductionvectorabstract algebraalgebrapolynomial