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## How many integers must you pick in order to be sure that at least two of them have the same remainder when divided by 15?

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Math High School
4 weeks
2022-12-24T07:06:31+00:00
2022-12-24T07:06:31+00:00 1 Answer
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## Answer ( 1 )

choose16 integers in such a way that we can ensure that when they are divided by 15, at least two of them will provide the sameresidual.## How many integers must you pick in order to be sure that at least two of them have the same remainder when divided by 15?

fraction. There are 15remaindersthat might occur, and they are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14.remaindermay be any of the 15 (0 reminders 14). Therefore, if we choose 15 numbers, we will have the opportunity to pick 15 uniquereminders, ranging from 0 to 14.integer, that is we pick 16 integers, then at least two of them would have the same reminder since there are only 15 reminders and 16>15, and by thepigeonholeprinciple.dividedby 15.integershttps://brainly.com/question/15276410