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There are exactly four positive integers such that (n + 1)^2/(n + 27) is an integer. Compute the largest such n.

 Apr 18, 2022
 #1
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There are 4 integer value of n as follows:

 

n ==13,  121,  288, 625 [The largest such number]

 Apr 19, 2022
 #2
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The above 4 numbers are NOT correct! The following 4 numbers are correct:

 

n = 25, 142, 311, 649

 

Therefore, the largest n=649

 Apr 19, 2022

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