■ユークリッドの互除法(その4)

 モジュラー算術では

  a=b (modm),cは整数

→a+c=b+c (modm),ac=bc (modm)

  a=b (modm),c=d (modm)

→a+c=b+d (modm),ac=bd (modm)

  a=b (modm)

→a^2=b^2,a^3=b^3,・・・,a^n=b^n (modm)

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13=4 (mod9)

16=-2 (mod9)

2つの合同式を足すと

29=2 (mod9)

2つの合同式をかけると

208=-8 (mod9)

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