规定符号f(x)(x是正整数)满足下列性质:(1)当x=1时,f(1)=0 (2)当x=p(p为质数)时,f(p)=1(1)当x=1时,f(1)=0 (2)当x=p(p为质数)时,f(p)=1 (3)对任意两个正整数m,n,有f(m*n)=mf(n)+nf(m
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![规定符号f(x)(x是正整数)满足下列性质:(1)当x=1时,f(1)=0 (2)当x=p(p为质数)时,f(p)=1(1)当x=1时,f(1)=0 (2)当x=p(p为质数)时,f(p)=1 (3)对任意两个正整数m,n,有f(m*n)=mf(n)+nf(m](/uploads/image/z/9760761-9-1.jpg?t=%E8%A7%84%E5%AE%9A%E7%AC%A6%E5%8F%B7f%EF%BC%88x%29%28x%E6%98%AF%E6%AD%A3%E6%95%B4%E6%95%B0%EF%BC%89%E6%BB%A1%E8%B6%B3%E4%B8%8B%E5%88%97%E6%80%A7%E8%B4%A8%EF%BC%9A%EF%BC%881%EF%BC%89%E5%BD%93x%3D1%E6%97%B6%2Cf%EF%BC%881%EF%BC%89%3D0+%EF%BC%882%EF%BC%89%E5%BD%93x%3Dp%28p%E4%B8%BA%E8%B4%A8%E6%95%B0%EF%BC%89%E6%97%B6%2Cf%EF%BC%88p%EF%BC%89%3D1%EF%BC%881%EF%BC%89%E5%BD%93x%3D1%E6%97%B6%2Cf%EF%BC%881%EF%BC%89%3D0+%EF%BC%882%EF%BC%89%E5%BD%93x%3Dp%28p%E4%B8%BA%E8%B4%A8%E6%95%B0%EF%BC%89%E6%97%B6%2Cf%EF%BC%88p%EF%BC%89%3D1+%EF%BC%883%EF%BC%89%E5%AF%B9%E4%BB%BB%E6%84%8F%E4%B8%A4%E4%B8%AA%E6%AD%A3%E6%95%B4%E6%95%B0m%2Cn%2C%E6%9C%89f%28m%2An%29%3Dmf%28n%29%2Bnf%28m)
规定符号f(x)(x是正整数)满足下列性质:(1)当x=1时,f(1)=0 (2)当x=p(p为质数)时,f(p)=1(1)当x=1时,f(1)=0 (2)当x=p(p为质数)时,f(p)=1 (3)对任意两个正整数m,n,有f(m*n)=mf(n)+nf(m
规定符号f(x)(x是正整数)满足下列性质:(1)当x=1时,f(1)=0 (2)当x=p(p为质数)时,f(p)=1
(1)当x=1时,f(1)=0 (2)当x=p(p为质数)时,f(p)=1 (3)对任意两个正整数m,n,有f(m*n)=mf(n)+nf(m),求f(2010)-2010的值
规定符号f(x)(x是正整数)满足下列性质:(1)当x=1时,f(1)=0 (2)当x=p(p为质数)时,f(p)=1(1)当x=1时,f(1)=0 (2)当x=p(p为质数)时,f(p)=1 (3)对任意两个正整数m,n,有f(m*n)=mf(n)+nf(m
我做出来是97.过程是一步一步按2010=2*3*5*67进行分解,细致一点很容易得到答案.
2012=2*3*5*67
f(2010)-2010=2+3+5+67=-1933
我搞错了,他对的
f(2010)-2010=f(67*30)-2010=67*f(30)+30*f(67)-2010=67*f(2*15)-1980=67*(15*f(2)+2*f(15))-1980=67*(15+2*(f(3*5)))-1980=67*(15+2*(3*f(5)+5*f(3)))-1980=67*31-1980=97
f(p)不是等于1么,还能够有30*67!?难道我看错了- -
f(2010)-2010=f(30×67)-2010=30f(67)+67f(30)-2010=30×67+67f(5×6)-2010=67[5f(6)+6f(5)]=335f(2×3)+402×5=335[2f(3)+3f(2)]+2010=670×3+1005×2+2010=6030。