Re: 幫個忙否?

[hiei81 (寶貝。永遠)]

※ 引述《chaogold (H.Y. Chao)》之銘言：
: 1.Find all integers  n>=1 such that
: (n^3+3)/(n^2+7)is an intege

(n^2+7)|(n^3+7n) => (n^2+7)|(7n-3)
=> n<=5 => n=2,5

: 2.Find all integral values of x,y,z,w given
:  that  x!+y!=2^z*3^w

Consider x>0, y>0

WLOG, assume x>=y
Note y<5 otherwise 5|2^z+3^w
if y=1 => x=1 or 2 since if x>=3 then (2,x!+1)=(3,x!+1)=1
       => (1,1,1,0) or (2,1,0,1) (reverse x,y => (1,2,0,1))
if y=2 => if x=2 or 3 then z>1 if x>=4 then z=1 => 3|(x!/2+1) -><-
       => (2,2,2,0) or (3,2,3,0) (2,3,3,0)
if y=3 => if x>=6 then w=1 => 2|(x!/6+1) -><- so x<=5
       => (3,3,2,1)
if y=4 => if x>=6 then z=3 => 3|(x!/24+1)-><- so x<=5
       => (4,4,4,1) or (5,4,4,2) (4,5,4,2)
共10組解

: 3.Let f (x) be a linear function such that
: f(0)=–5 and f(f(0)) =–15.

Let f(x)=ax+b => b=-5, a=2

: Find all values of m for which the solutions
: of the inequality f(x)f(m–x)> 0  form an
:  interval of length 2.

=>(2x-5)(-2x+2m-5)>0 => (x-5/2)(x-(5/2 -m))<0
=>5/2-m = 5/2 +- 2 => m=2,-2 (好怪的題目?)

: ----
: 有人問我的
: 有誰可以幫忙解一下?

--
                       濃濃的感情甜蜜，
               淡淡的感情長流，
                    愛情得在這濃濃的、淡淡的感覺中
                        交織出無上的光芒

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 24.215.219.96
推 chaogold:恩恩 那個滿怪的