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為了方便起見,現將本文中所用的幾個記號加以說明,並將涉及到的幾個整數性質加以叙述而不予證明。另外,凡本文中所用之字母,如a,b,c,…,若不加說明,皆指正整數而言。 幾個記號:(a_1,a_2,…,a_n)表示a_1,a_2,…,a_n的最大公約數;[a_1,a_2,…,a_n]表示a_1,a_2,…,a_n的最小公倍數,a|b表示a能除盡b。涉及到的幾個整數性質: Ⅰ. 若a,b為任何正整數,則ab-(a+b)≥-1。Ⅱ. 若(a_1,a_2,…,a_n)=d_n,則a_1=a′_1d_n,a_2=a′_2 d_n,…,a_n=a′_nd_n,且(a′_1,a′_2,…,a′_n)=1。Ⅲ. 若[a,b]=m,a|c,b|c,則m|c。Ⅳ. 如果在全是整數的等式k+l+…+n=p+q+…+s中,所有的項,除掉一項外,都是b的倍數,則這一項也一定是b的倍數(即b能除盡這一項)。
For the sake of convenience, several symbols used herein are described, and several integer properties involved are described without certifying. In addition, the letters used in this article, such as a, b, c, ..., are positive integers unless otherwise specified. A few tokens: (a_1, a_2, ..., a_n) denote the greatest common divisor of a_1, a_2, ..., a_n; [a_1, a_2, ..., a_n] denote the least common multiple of a_1, a_2, ..., a_n, a|b Indicates that a can divide b. Several integer properties are involved: I. If a, b is any positive integer, ab-(a+b)≥-1. II. If (a_1,a_2,...,a_n)=d_n, a_1=a′_1d_n, a_2=a′_2 d_n,...,a_n=a′_nd_n, and (a′_1, a′_2,...,a ’_n)=1. III. If [a,b]=m,a|c,b|c, then m|c. IV. If all the integers in the equation k+l+...+n=p+q+...+s, all items except one, are multiples of b, then this item must also be b. Multiple (ie b can divide this one).