Maritza's car has 16 gallons of gas in the tank. She uses 3/4 of the gas. How many gallons of gas does Maritza use?
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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 such that
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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