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Let n be a positive integer. Let R be the remainder when \(n^2\) is divided by n+4. How many different values can R take on?

 

(Please explain how you got your answer thoroughly)

 Apr 12, 2020
 #1
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n^2 is divisible by n + 4 only for n = 4 and n = 12, so there are two possible values of n.

 Apr 12, 2020
 #2
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Do it brute force, entering all positive integers n in order until reaching 13 (n=3, remainder 2, n=4, remainder 0, etc.). All numbers 'n' greater than or equal to 13 will have a remainder of 16, so when discarding the two remainders that repeat (2 and 0) the answer is 9.

 Apr 14, 2020

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