ナルシシスト数について
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概要
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This paper is devoted to generalization of narcissistic number. Let n be a natural number and n = ΣlO^iq_i be the decimal representation, and p>1 be a natural number. Then, n is called a generalized narcissistic number for p if Σq^p_i = n, and p is called as index of narcissistic number. We prove the following theorems : Theorem 1. Narcissistic numbers with index 3 are 1,153,370,371 and 407. Theorem 2. Number of generalized narcissistic numbers with index p are finite. In the proof of Theorem 2,we have the following inequality : (n-log (n+1))/log 9 <n , which concerns an upper bound of index p.