MathDB

A subset

S

of the set

M=\{1,2,.....,p-1\}

,where

p

is a prime number of the kind

12n+11

,is essential,if the product

{\Pi}_s

of all elements of the subset is not less than the product

\bar{{\Pi}_s}

of all other elements of the set.The difference

\bigtriangleup_s=\Pi_s-\bar{{\Pi}_s}

is called the deviation of the subset

S

.Define the least possible remainder of division by

p

of the deviation of an essential subset,containing

\frac{p-1}{2}

elements.

Problem Statement