MathDB

sum indivisible by prime

Source: miklos schweitzer 1992 q2

October 22, 2021

number theorycombinatorics

Problem Statement

Let p be a prime and

a_1 , a_2 , ..., a_k

pairwise incongruent modulo p . Prove that

[\sqrt {k-1}]

of the elements can be selected from

a_i

's such that adding any numbers different from the selected ones will never give a number divisible by p .