MathDB

Let

p

be a prime number. For each

k

1\le k\le p-1

, there exists a unique integer denoted by

k^{-1}

such that

1\le k^{-1}\le p-1

and

k^{-1}\cdot k=1\pmod{p}

. Prove that the sequence 1^{-1}, 1^{-1}+2^{-1}, 1^{-1}+2^{-1}+3^{-1}, \ldots , 1^{-1}+2^{-1}+\ldots +(p-1)^{-1} (addition modulo

p

) contains at most

\frac{p+1}{2}

distinct elements.

Problem Statement