MathDB

35

Part of PEN A Problems

Problems(1)

A 35

Source:

5/25/2007
Let p≥5p \ge 5 be a prime number. Prove that there exists an integer aa with 1≤a≤p−21 \le a \le p-2 such that neither ap−1−1a^{p-1} -1 nor (a+1)p−1−1(a+1)^{p-1} -1 is divisible by p2p^2.
modular arithmeticDivisibility Theory