October 28th, 2013, 02:57 AM  #1 
Member Joined: Nov 2012 Posts: 61 Thanks: 0  maximum value
If a,b are natural numbers such that then the maximum possible value of ab is

October 28th, 2013, 03:31 AM  #2 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: maximum value
Here is an 'intuitive' approach. The difference between consecutive integer squares is in arithmetic progression of the odd integers. . . . So we want 2n + 1 = 2013 which makes n = 1006 ab = 1006*1007 = 1013042 This is the maximum since it gives WE can't do better than that because there are no integer squares between consecutive integer squares. 
November 8th, 2013, 02:29 AM  #3 
Member Joined: Nov 2012 Posts: 61 Thanks: 0  Re: maximum value
Can you tell what will be the minimum value?


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