Problem: For every odd number p>1 we have:
Answer Choices:
A. (p−1)21(p−1)−1 is divisible by p−2
B. (p−1)21(p−1)+1 is divisible by p
C. (p−1)21(p−1) is divisible by p
D. (p−1)21(p−1)+1 is divisible by p+1
E. (p−1)21(p−1)−1 is divisible by p−1
Solution:
Since p is odd and p>1, then 21(p−1)≥1. In every case one factor of (p−1)21(p−1)−1 will be [(p−1)−1]=p−2. The other choices are either possible only for special permissible values of p or not possible for any permissible values of p.