Answer to Question #279372 in Combinatorics | Number Theory for Jaishree

Question

Show that among any group of five (not necessarily consecutive) integers, there

are two with the same remainder when divided by 4

Answer 1

every integer can be expressed as

$4k,4k+1,4k+2,4k+3$

where k = 0,1,2,...

so, if we have 5 integers two of them have same remainder