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家住美国中西部一个小城市的史密斯是一个数学门外汉。他家有一部电话,其号码是七位数4937775。一天,他把电话号码分解为素数因数连乘积:4937775=3×5×5×65837,然后把上面所有素数因数(不含1)3,5,5,65837的各位数字相加,即3+5+5+6+5+8+3+7=42。当然,也可将42再施以各位数相加,4+2=6。他又把4937775各位数相加:4+9+3+7+7+7+5=42。(同上,4+2=6)他眼前一亮,发现两者之和居然相等。这真有意思,难道是巧合吗?有没有其他的数也有此特点呢?史密斯不能解答这个问题。于是他将这一发现告诉他的数学家亲戚维伦斯基。数学
Smith, a small city in the Midwestern United States, is a math layman. His family has a phone whose number is seven digits 4937775. One day, he divided the phone number into prime factors and multiplied them by the product: 4937775 = 3 × 5 × 5 × 65837, and added all the above figures of prime factors (excluding 1) 3,5,5,65837, that is, 3+ 5 + 5 + 6 + 5 + 8 + 3 + 7 = 42. Of course, 42 can be applied to the same digit, 4 +2 = 6. He added the digits 4937775 to each other: 4 + 9 + 3 + 7 + 7 + 7 + 5 = 42. (Ibid, 4 + 2 = 6) He shines and finds that the sum of the two is actually the same. Is this a coincidence? Is there any other number that has this feature too? Smith can not answer this question. So he told this discovery to his mathematician relatives Virlenski. mathematics