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用反證法: 假設素數是有限的,我們可以用p1,p2,……,pn來表示這些素數 其他任何一個數都是複合數,且素數p1,p2,……,pn中至少有一個能够整除它 構造一個數A,讓它比p1,p2,……,pn中任一個都大,從而與它們中的任一個都不同 令A=p1p2×……×pn+1 但A不能被p1,p2,……,pn中任一個整除,所以A是素數,這與素數只有p1,p2,……,pn衝突 囙此素數是無窮多的
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