Question

Given that $p\ge 7$ is a prime number, evaluate $$1^{-1} \cdot 2^{-1} + 2^{-1} \cdot 3^{-1} + 3^{-1} \cdot 4^{-1} + \cdots + (p-2)^{-1} \cdot (p-1)^{-1} \pmod{p}.$$

Answer 1

Since p is odd, the negatives of the odd residues listed in your product are the even residues: − 1 = p − 1( mod p ), − 3 = p. since we are working modulo p.

It includes prime number that takes an integer P>1 and divisors and takes 1 and p.

It denotes prime factor and taking multiple inverses and includes elements lists of prime number.