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Find all integers n such that n^3 = (n - 1)^3 + 37.

 
 Sep 10, 2021
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Find all integers n such that n^3 = (n - 1)^3 + 37.     

 

I found two by brute force, i.e., n = 4 and n = –3  

 

check n = 4 

n3 = (n – 1)3 + 37   

43 = 33 + 37  

64 = 27 + 37  

 

You can check n = –3 yourself, if you like.   

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 Sep 10, 2021

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