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下象棋的人很少思考为什么馬走“日”?下面的定理1似乎可以启发我們思考。然后我們用“狂馬跳步”証明几何上的一个定理。定义1.一个馬称为(m,n)广义馬,如果它在平面坐标格点)上跳跃于边长分别为m,n的矩形的对角頂点。自然,象棋馬为(1,2)馬(或(2,1)馬)。以下我們說到点都指的是格点。定义2.(m,n)广义馬称为是“遍及”的,如果它在有限步内可从一点跳到任意的另一点。定理1.一个(m,n)广义馬是遍及的,当且仅当m,n互素,且一奇一偶。证.不失一般性,令馬位于(0,0)点.(m,n)广义馬是遍及的等价于馬可在有限步内由(0,0)跳至(0,1)(簡記为(0,0)→(0,1))。设經a+b步有(0,0)→(0,1),其中a,b滿足
People who play chess rarely think about why the horse takes the “day.” The following Theorem 1 seems to inspire us to think. Then we prove a theorem of geometry with “mad horse jump.” Definition 1. A horse is called a (m,n) generalized horse if it jumps on a plane coordinate grid point) to the diagonal vertices of rectangles whose sides are respectively m,n. Naturally, chess horses are (1,2) horses (or (2,1) horses). Here we say that the points all refer to grid points. Definition 2. (m,n) The generalized horse is said to be “over” if it can jump from one point to another at a different point in a finite step. Theorem 1. A (m,n) generalized horse is ubiquitous, if and only if m, n are mutually prime, and odd and even. With no loss of generality, the horse is located at the (0,0) point. (m,n) Generalized horse is ubiquitous and is equivalent to Marco jumping from (0,0) to (0,1) in a limited step ( Abbreviated as (0,0)→(0,1)). Suppose there is (0,0)→(0,1) in a+b step, where a,b is satisfied