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February 12th, 2013, 05:17 PM  #1 
Newbie Joined: Feb 2013 Posts: 1 Thanks: 0  Translating Algorithm into Math?
Hello. This is my first posting here, so I am not sure this is in the correct place. I have this math problem: Find the number of distinct integers in this set: [ (1^2) / 5012 ] , [ (2^2) / 5012 ] , ...... , [ (5012^2) / 5012 ] where [ x ] denotes the greatest integer less than or equal to x. I am not very familiar with the mathematical notation involved with this problem, so I wrote a computer program that solves it (in Java): Code: double t[] = new double[5013]; Set<Integer> distinct = new HashSet<Integer>(); for (int i = 1; i <= 5012; i++) { double q = Math.pow(i, 2); int l = (int) Math.floor(q / 5012); //gets "X" (greatest integer <= x) t[i] = l; distinct.add(l); } System.out.println(distinct); System.out.println("SIZE: " + distinct.size()); But I do not know how to represent this mathematically. Any help is appreciated! Thank you. 

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