When the optimistic integer "n" is split by 3, the remainder is 2 and also when "n" is separated by 5, the remainder is 1. What is the least feasible value that "n"? The answer is 11. My concern is, if you have actually very huge numbers to job-related with in this problem, what would certainly be the quickest and easiest way to calculate this quickly? give thanks to you for your time and also attention to mine question.

You are watching: When positive integer n is divided by 3 the remainder is 2 Chinese remainder theorem.

Basic solution.

LCM(3,5)=15

If we divide by 3 and also the remainder is 2, the feasible remainders when splitting by 15 are 2, 5, 8, 11, and 14.

If we divide by5 and the remainder is 1, the feasible remainders when dividing by 15 room 1, 6,and 11.

So all options are 15n+11 and also 11 is the smallest.

Chinese remainder to organize solution.

Again LCM(3,5)=15.

The smallest multiple of3and remainder 1 when separating by5 is A=6 and the smallest multiple that 5 v remainder 1 when separating by 3 is B=10.

Dividing A+2B=26 through 15 provides remainder 11.

So again all solutions are 15n+11 and also 11 is the smallest.

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Linda C.

Thank you, Roman. This is a good answer. Give thanks to you so much!! Linda

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