Question

Problem 7. Show that among any four numbers one can find at least two numbers so that their difference is divisible by 3. las i visible mig any four

Answer 1

Answer:

Explained

Step-by-step explanation:

let there be $a_{1} , a_{2}, a_{3}, a_{4}$ any four integers.

when dividing any integer by 3 there 3 remainders  {0,1,2}

Now since there are 4 numbers and 3 integers certainly there be 2 numbers with same remainder when divided by 3.

that is there exist $a_{i} and a_{j}$

$a_{i}=3m+r$

$a_{j}=3n+r$

where m and n are integers and $r\in{0,1,2}$

$a_{i}-a_{j}=3m+r-3n-r=3(m+n)$

thus their difference is divisible by 3