Problems(1)
Let p be an arbitrary odd prime and σ(n) for 1≤n≤p−1 denote the inverse of n(modp). Show that the number of pairs (a,b)∈{1,2,⋯,p−1}2 with a<b but σ(a)>σ(b) is at least ⌊(4p−1)2⌋usjlNote: Partial credits may be awarded if the 4 in the statement is replaced with some larger constant number theory