Answer:There are two integers in the group of n+1 integers with exactly the same remainder when they are divided by n.
Explanation:
Generally, if a number is divided by p(positive integer), then the possible remainders will be from 0 to p-1.
Here, the possible remainders when an integer is divided by n are 0,1,....,n-1
so the number of possible remainders when an integer is divided by n is n.
In this case, the number of objects is n+1 integers and the number of boxes (remainders) is n.
p/k = (n+1)/n
= 1+(1/n)
= 2
Here, 0<1/n<1
Add 1 on both sides to get the following
0+1 < 1+1/n<1+1
1<1+1/n<2
so the value of p/k = 2 means that there is atleast one remainder which is same for two integers when they are divided by n
There are therefore two integers in the group of n+1 integers with exactly the same remainder when they are divided by n.
