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What is the largest positive integer n for which n^3+100 is divisible by n+1?

 
 Jan 13, 2021
 #1
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23+100=108

2+1=3

108/3=36

 

answer is 2

 
 Jan 13, 2021
 #2
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What is the largest positive integer n for which n^3+100 is divisible by n+1?

 

n^3 + 100 mod (n +1) =

(98^3 + 100)  mod (98 + 1) =

941,292 mod 99 == 0

 
 Jan 14, 2021

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