Re: [離散]鴿籠原理

[JohnMash (John)]

※ 引述《MeNeNe (咪逆逆)》之銘言：
: 1.設a,b,c,d是任意給定的四個整數，求證
:     (b-a)(c-a)(d-a)(c-b)(d-b)(d-c)被12整除。


      let b-a=i, c-a=j, d-a=k

      then c-b=j-i, d-b=k-i, d-c=k-j

      A=ijk(j-i)(k-i)(k-j)

   if i,j,k are all odd

   then (j-i), (k-i), (k-j) are all even

   then A=0 (mod4)

   if two of i,j,k are odd,

   then one of i,j,k is even

   and one of (j-i), (k-i), (k-j) is even

   then A=0 (mod4)


   A=0 (mod3) exercise

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 112.104.97.47
推 hchuang     :exercise ...XD