Question

What is the least amount of integers you must pick in order to be sure that at least two of them have the same remainder when divided by 15

Answer 1

There are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.

It is given that at least two of them should have the same remainder when divided by 15.

Division algorithm.

Let aa be an integer and d a positive integer. Then there are unique integers q and r with $0\leq r < d$ such that $a=dq+r$

q is called the quotient and r is called the remainder

q=a div d

r=a mod d

Pigeonhole principle If k is a positive integer and k+1or more objects are placed into k boxes, then there is at least one box containing two or more objects.

Hence, there are exactly 15 remainders modulo 15 and they are 0,1,2,…,14.

Learn more about integers here: brainly.com/question/20521181

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