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April 11th, 2018, 12:29 AM  #1 
Member Joined: Apr 2018 From: On Earth Posts: 34 Thanks: 0  Is there a method to solve these types of questions?
With questions such as: Find all values of n such that both expressions are integers n and n+16/n+1 2n and 7/n etc... Is there a method in which this can be solved without trial and error? Thanks 
April 11th, 2018, 03:37 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,511 Thanks: 1743 
No. Let's take the second problem as an example. Let m = 2n, so that m is required to be an integer. As 7/n = 14/m is also required to be an integer, we know that m divides 14. It follows (by trial and error) that m = ±1, ±2, ±7 or ±14. Hence n = ±1/2, ±1, ±7/2 or ±7. 

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