October 2015

Happy 2012/2004

• Author: rin
• Time: October 24, 2015
• Classification: Algo
• comment

<trans data-src="[">[</trans> <trans data-src="http://acm.bjfu.edu.cn/acmhome/problemdetail.do?&method=showdetail&id=1087">http://acm.bjfu.edu.cn/acmhome/problemdetail.do?&method=showdetail&id=1087</trans> <trans data-src="](">](</trans> <trans data-src="http://acm.bjfu.edu.cn/acmhome/problemdetail.do?&method=showdetail&id=1087">http://acm.bjfu.edu.cn/acmhome/problemdetail.do?&method=showdetail&id=1087</trans> <trans data-src=" ""> "</trans> <trans data-src="http://acm.bjfu.edu.cn/acmhome/problemdetail.do?&method=showdetail&id=1087">http://acm.bjfu.edu.cn/acmhome/problemdetail.do?&method=showdetail&id=1087</trans> <trans data-src="")">")</trans> <trans data-src="###描述">###Description</trans> <trans data-src="Consider a positive integer X,and let S be the sum of all positive integer divisors of 2012^X. Your job is to determine S modulo 29 (the rest of the division of S by 29).">Consider a positive integer X,and let S be the sum of all positive integer divisors of 2012^X. Your job is to determine S modulo 29 (the rest of the division of S by 29).</trans> <trans data-src="Take X = 1 for an example. ">Take X = 1 for an example. </trans> <trans data-src="The positive integer divisors of 2012^1 are 1, 2, 4, 503, 1006 and 2012. ">The positive integer divisors of 2012^1 are 1, 2, 4, 503, 1006 and 2012. </trans> <trans data-src="Therefore S = 3528 and S modulo 29 is equal to 19.">Therefore S = 3528 and S modulo 29 is equal to 19.</trans> <trans data-src="###输入">###Input</trans> <trans data-src="The input consists of several test cases. ">The input consists of several test cases. </trans> <trans data-src="Each test case contains a line with the integer X (1 <= X <= 1000000).">Each test case contains a line with the integer X (1 <= X <= 1000000).</trans> <trans data-src="A test case of X = 0 indicates the end of input, and should not be processed.">A test case of X = 0 indicates the end of input, and should not be processed.</trans> <trans data-src="###输出">###Output</trans> <trans data-src="For each test case, in a separate line, please output the result of S modulo 29.">For each test case, in a separate line, please output the result of S modulo 29.</trans> <trans data-src="###样例输入">###Sample Input</trans> <trans data-src="```">```</trans> <trans data-src="1">one</trans> <trans data-src="100000">one hundred thousand</trans> <trans data-src="```">```</trans> <trans data-src="###样例输出">###Sample Output</trans> <trans data-src="```">```</trans> <trans data-src="19">nineteen</trans> <trans data-src="2">two</trans> <trans data-src="```">```</trans> <trans data-src="题目大意是  给定一个$$X$$，求$$2012^{X}$$所有因数的和，结果模上29">Given a $$X $$, find the sum of all factors of $$2012 ^ {X} $$, and the result module is 29</trans> <trans data-src="记 $$S(n)$$ 为 $$n$$ 的所有因数之和，有：">Record $$S (n) $$as the sum of all factors of $$n $$, including:</trans> <trans data-src="```math">```math</trans> <trans data-src="\begin{array}{l}">\begin{array}{l}</trans> <trans data-src="S(2)=1+2=3 \\">S(2)=1+2=3 \\</trans> <trans data-src="S(3)=1+3=4 \\">S(3)=1+3=4 \\</trans> <trans data-src="S(4)=1+2+4=7 \\">S(4)=1+2+4=7 \\</trans> <trans data-src="S(5)=1+5=6 \\">S(5)=1+5=6 \\</trans> <trans data-src="S(6)=1+2+3+6=12 \\">S(6)=1+2+3+6=12 \\</trans> <trans data-src="S(7)=1+7=8 \\">S(7)=1+7=8 \\</trans> <trans data-src="S(8)=1+2+4+8=15 \\">S(8)=1+2+4+8=15 \\</trans> <trans data-src="S(9)=1+3+9=13 \\">S(9)=1+3+9=13 \\</trans> <trans data-src="S(10)=1+2+5+10=18 \\">S(10)=1+2+5+10=18 \\</trans> <trans data-src="\qquad ... \\">\qquad ... \\</trans> <trans data-src="S(14)=1+2+7+14=24 \\">S(14)=1+2+7+14=24 \\</trans> <trans data-src="S(15)=1+3+5+15=24 \\">S(15)=1+3+5+15=24 \\</trans> <trans data-src="S(16)=1+2+8+16=27 \\">S(16)=1+2+8+16=27 \\</trans> <trans data-src="\qquad \cdots \\">\qquad \cdots \\</trans> <trans data-src="S(24)=1+2+3+4+6+8+12+24=60 \\">S(24)=1+2+3+4+6+8+12+24=60 \\</trans> <trans data-src="\qquad \cdots \\">\qquad \cdots \\</trans> <trans data-src="S(30)=1+2+3+5++6+10+15+30=72 \\">S(30)=1+2+3+5++6+10+15+30=72 \\</trans> <trans data-src="\qquad \cdots \\">\qquad \cdots \\</trans> <trans data-src="\end{array}">\end{array}</trans> <trans data-src="```">```</trans> <trans data-src="由<ruby>  观察  <rt> naodong </rt></ruby>有：">From<ruby>observation<rt>naodong</rt></ruby>there are:</trans> <trans data-src="```math">```math</trans> <trans data-src="\begin{array}{l}">\begin{array}{l}</trans> <trans data-src="\qquad \cdots \\">\qquad \cdots \\</trans> <trans data-src="S(6)=S(2)\times S(3)=12 \\">S(6)=S(2)\times S(3)=12 \\</trans> <trans data-src="S(10)=S(2)\times S(5)=18 \\">S(10)=S(2)\times S(5)=18 \\</trans> <trans data-src="S(14)=S(2)\times S(7)=24\\ ">S(14)=S(2)\times S(7)=24\\ </trans> <trans data-src="S(15)=S(3)\times S(5)=24\\ ">S(15)=S(3)\times S(5)=24\\ </trans> <trans data-src="S(24)=S(3)\times S(8)=60">S(24)=S(3)\times S(8)=60</trans> <trans data-src="\end{array}">\end{array}</trans> <trans data-src="```">```</trans>

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• Author: rin
• Time: October 10, 2015
• Classification: Unclassified
• 6 comments

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