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April 8th, 2014, 02:47 AM  #1 
Senior Member Joined: Oct 2013 From: Far far away Posts: 429 Thanks: 18  Prove or disprove
Prove or disprove the claim that for any positive integer m there is a positive integer n such that mn + 1 is a perfect square My attempt: After trying out a few concrete examples I noticed that n has to be m + 2 So here's my proof Let n = m + 2 so mn + 1 = m(m + 2) + 1 = m^2 + 2m + 1 = (m + 1)^2 So for every m there exists an n such that n = m + 2 that makes mn + 1 a perfect square. Is this proof acceptable? Is there a better way? thanks 
April 8th, 2014, 03:04 AM  #2 
Senior Member Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra 
Your proof is correct. 

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