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February 15th, 2010, 12:24 PM  #1 
Member Joined: Jul 2009 Posts: 88 Thanks: 0  the largest integer number , let [x] be the largest integer less than or equal to x . prove that : 
February 15th, 2010, 12:55 PM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: the largest integer number
Let x = a² + b + c, where a² is the largest square number less than or equal to x, b is [x]a², and c is x[x]. So a and b are integers, and 0 ? c < 1. Then [x] = a²+b, and you should be able to show that a ? ?(a²+b) ? ?x < a+1.

March 1st, 2010, 02:25 AM  #3 
Member Joined: Jul 2009 Posts: 88 Thanks: 0  Re: the largest integer number __________________________________  i really don't know ! 
March 1st, 2010, 07:24 PM  #4 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: the largest integer number
a² ? a²+b ? a²+b+c < (a+1)² But a²+b = [x] so a² ? [x] ? x < (a+1)² and take square roots 

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