问题及解答

如何用连分数求解二元一次不定方程 $119x-32y=1$?

使用 Calculator 我们可以这样操作:

>> continued_fraction(119/32)
in> continued_fraction(119/32)

out> (3,1,2,1,1,4)

------------------------

>> continued_fraction(3,1,2,1,1)
in> continued_fraction(3,1,2,1,1)
out> 26|7

Expression:
3+1/(1+1/(2+1/(1+1/(1))))

TeX Code:
3+\frac{1}{1+\frac{1}{2+\frac{1}{1+\frac{1}{1}}}}

------------------------

>> 119*7-32*26
in> 119*7-32*26

out> 1

也可以利用 IndefiniteEquation() 函数.

>> IndefiniteEquation(119,-32)
in> IndefiniteEquation(119,-32)
Solve the equation: 119*x-32*y = 1
119==3*32+23
32==1*23+9
23==2*9+5
9==1*5+4
5==1*4+1
3 1 2 1 1
test: -1==2*6-9*7
119*7-32*26 == 1
x = 7+32t
y = 26+119t