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February 15th, 2010, 12:24 PM   #1
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the largest integer number

, let [x] be the largest integer less than or equal to x . prove that :
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February 15th, 2010, 12:55 PM   #2
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Re: the largest integer number

Let x = a + b + c, where a is the largest square number less than or equal to x, b is [x]-a, and c is x-[x]. So a and b are integers, and 0 ? c < 1. Then [x] = a+b, and you should be able to show that a ? ?(a+b) ? ?x < a+1.
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March 1st, 2010, 02:25 AM   #3
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Re: the largest integer number





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i really don't know !
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March 1st, 2010, 07:24 PM   #4
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Re: the largest integer number

a ? a+b ? a+b+c < (a+1)
But a+b = [x] so
a ? [x] ? x < (a+1)
and take square roots
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