※ 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 --

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