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The marching band has more than 100 members but fewer than 200 members. When they line up in rows of 4 there is one extra person; when they line up in rows of 5 there are two extra people; and when they line up in rows of 7 there are four extra people. How many members are in the marching band?

 Dec 11, 2020
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N mod 4==1

N mod 5==2

N mod 7==4

 

Using Chinese Remainder Theorem + Modular Multiplicative Inverse, we have:

N==140m + 137, where m=0, 1, 2, 3.......etc.

Therefore, the smallest N==137 - number of students in a marching band.

 Dec 11, 2020

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