题目

f(x,x)=x f(x,y)=f(y,x) (x+y)f(x,y)=yf(x,x+y)求f(14,52)

提问时间：2021-03-18

答案

由题知,
f(x,x)=x f(x,y)=f(y,x) (x+y)f(x,y)=yf(x,x+y)
所以,
f(14,52)
=f(14,14+38)
=(52/38)f(14,38)
=(52/38)f(14,14+24)
=(52/38)(38/24)f(14,24)
=(52/24)f(14,14+10)
=(52/24)(24/10)f(14,10)
=(52/10)f(10,14)
=(52/10)f(10,10+4)
=(52/10)(14/4)f(10,4)
=(52/10)(14/4)f(4,10)
=(52/10)(14/4)f(4,4+6)
=(52/10)(14/4)(10/6)f(4,6)
=(52/10)(14/4)(10/6)f(4,4+2)
=(52/10)(14/4)(10/6)(6/2)f(4,2)
=(52/10)(14/4)(10/2)f(2,4)
=(52/2)(14/4)f(2,2+2)
=(52/2)(14/4)(4/2)f(2,2)
=(52/2)(14/4)(4/2)*2
=26*14
=364