■ファレイ分数(その9)
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)
===================================
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)
===================================