[中學] 集合相關
The set A={1,2,3,...,2044,2045} contains 2045 elements. A subset S of A is
called triple-free if no element of S equals three times another element
of S. For example, {1,2,4,5,10,2043} is triple-free, but
{1,2,4,5,10,681,2043} is not triple-free. The triple-free subsets of A that
contain the largest number of elements contain exactly 1535 elements.
There are n triple-free subsets of A that contain exactly 1535 elements.
The integer n can be written in the form p^a*q^b, where p and q are distinct
prime numbers and a and b are positive integers. If N=p^2+q^2+a^2+b^2,
then the last three digits of N are
(A)202 (B)102 (C)302 (D)402 (E)502
學生問的題目,剩這題沒想出來,只有想到1535是怎麼算出來的,但有多少個這樣的集合
暫時沒有頭緒,上來請教板友看看有沒有想法,謝謝!
--
※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 220.136.213.95
※ 文章網址: https://www.ptt.cc/bbs/Math/M.1458300037.A.83E.html
→
03/18 23:27, , 1F
03/18 23:27, 1F
討論串 (同標題文章)