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
2013年7月23日 星期二
2013年2月24日 星期日
一題多解
翻自己以前寫的網誌，升高一的時候利用數學歸納法證明
\[3|4^n-1 \forall n\in\mathbb{N}\]
現在所學越來越多，能用的工具也越來越多了
我發現這個命題可以推廣為
\[m-1|m^n-1 \forall n\in\mathbb{N}\]
其實證明用同餘就秒殺了
因為$m\equiv1(\text{mod }m-1)$
兩邊同時$n$次方，得$m^n\equiv1(\text{mod }m-1)$
\[3|4^n-1 \forall n\in\mathbb{N}\]
現在所學越來越多，能用的工具也越來越多了
我發現這個命題可以推廣為
\[m-1|m^n-1 \forall n\in\mathbb{N}\]
其實證明用同餘就秒殺了
因為$m\equiv1(\text{mod }m-1)$
兩邊同時$n$次方，得$m^n\equiv1(\text{mod }m-1)$
2013年1月24日 星期四
2012年12月11日 星期二
身分證字號驗證
這個語法可以驗證一個身分證字號是不是合法的
function out = checkId(id)
first = [10:17 34 18:22 35 23:29 32 30 31 33];
a = uint8(upper(id));
b = zeros(1,11);
b(1:2) = uint8(num2str(first(a(1)-64)));
b(3:11) = uint8(a(2:10))-48;
out = mod([1 9 8 7 6 5 4 3 2 1 1]*b',10);
function out = checkId(id)
first = [10:17 34 18:22 35 23:29 32 30 31 33];
a = uint8(upper(id));
b = zeros(1,11);
b(1:2) = uint8(num2str(first(a(1)-64)));
b(3:11) = uint8(a(2:10))-48;
out = mod([1 9 8 7 6 5 4 3 2 1 1]*b',10);
2012年10月31日 星期三
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