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There are exactly two(2) positive integers such that (n + 1)^3 / (n + 20) is an integer. What are the 2 integers?. Thank you for help.

 Apr 4, 2019
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( n + 1)^3  

  _______   simplifies  to       n^2   - 17n - 6869   +    343

    n + 20                                                    _____

                                                                   n + 20

 

6859   factors as 19^3

 

So....19^2   will divide 6859......so   

 

n + 20  = 19^2 

 

n = 19^2 - 20  =  341

 

Also....19^3 will divide 6859....so

 

n + 20  =  19^3

 

n =  19^3 - 20   = 6839

 

So.....the two positive integers are   n = 341    and n = 6839

 

 

cool cool cool

 Apr 5, 2019

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