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Australian AMC 2019 - Junior Question 28

AMC AUSTRALIA · Australian AMC 2019 - Junior

Question 28

When I divide an integer by 15, the remainder is an integer from 0 to 14. When I divide an integer by 27, the remainder is an integer from 0 to 26.
For instance, if the integer is 100 then the remainders are 10 and 19, which are different.
How many integers from 1 to 1000 leave the same remainders after division by 15 and after division by 27?