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如果你不懂扩展欧几里德算法,我可以举个例子##

Posted by 200593141 at 2007-07-13 14:56:28 on Problem 1061
我不擅长讲,只能举几个例子—
欧几里德扩展法举例:
22×□≡ 1 mod 31
	31=1×22+9	-1×22 ≡ 9   		     即  30×22≡ 9 mod 31
	22=2×9+4	22-2×(-1×22) ≡ 4 	     即    3×22≡ 4 mod 31
	 9=2×4+1	-1×22-2×(3×22) ≡ 1          即  24×22≡ 1 mod 31

28×□≡ 1 mod 75
	75=2×28+19	-2×28≡19		  即 73×28≡19 mod 75
	28=1×19+9	28-1×(-2×28)≡9	           即   3×28≡  9 mod 75
	19=2×9+1	(-2×28)-2×(3×38)≡1       即67×28≡ 1 mod 75

269×□≡ 1 mod 349
	349=1×269+80	    -1×269≡80                  即  -1×269
	269=3×80+29	   269-3×(-1×269)≡29   	      即  4×269
	  80=2×29+22	   (-1×269)-2×(4×269)≡22     即 -9×269
	  29=1×22+7	   (4×269)-1×(-9×269)≡7     即 13×269
	  22=3×7+1	   (-9×269)-3×(13×269)≡1    即-48×269 得 301

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