Let be the n-th non-square positive integer. Thus etc. For a positive real number x, denotes the integer closest to it by . If , where m is an integer, then define . For example, . Show that

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- May 6th 2012, 11:03 PMharryphamNumber theory
Let be the n-th non-square positive integer. Thus etc. For a positive real number x, denotes the integer closest to it by . If , where m is an integer, then define . For example, . Show that