m个1组成的数11..1 %m等于1（这个命题是错误的，没法证明）

```julia> map(getg,[3,7,9,11])
4-element Array{Int64,1}:
4
7
10
3
```

m=5,10,命题也成立，但当m是大于10的10的幂时，一定不成立，比如m=100,因为m个1=(m-2)个1*100+11，余数为11。

```julia> map(x->(x,div(BigInt(10)^x-1,9)%x),primes(2,100))
25-element Array{Tuple{Int32,BigInt},1}:
(2,1)
(3,0)
(5,1)
(7,1)
(11,1)
(13,1)
(17,1)
(19,1)
(23,1)
(29,1)
(31,1)
(37,1)
(41,1)
(43,1)
(47,1)
(53,1)
(59,1)
(61,1)
(67,1)
(71,1)
(73,1)
(79,1)
(83,1)
(89,1)
(97,1)
```

```julia> map(x->(x,getg(x)),primes(7,100))
22-element Array{Tuple{Int32,Int64},1}:
(7,7)
(11,3)
(13,7)
(17,17)
(19,19)
(23,23)
(29,29)
(31,16)
(37,4)
(41,6)
(43,22)
(47,47)
(53,14)
(59,59)
(61,61)
(67,34)
(71,36)
(73,9)
(79,14)
(83,42)
(89,45)
(97,97)
```

np % p == n % p

10p % p == 10 % p

(p个9) % p == 9 % p

9 % p (p个1) % p == 9 % p 1 % p

(p个1) % p == 1 % p =1,证毕。

```julia> 1.0/7
0.14285714285714285

julia> 142857*7
999999

julia> 1.0/13
0.07692307692307693

julia> 76923076923*13
999999999999

julia> 1.0/17
0.058823529411764705

julia> BigFloat(1.0)/17
[5.88235294117647]058823529411764705882352941176470588235294117647058823529411765e-02

julia> BigFloat(1.0)/23
[4.347826086956521739130]43478260869565217391304347826086956521739130434782608698e-02

julia> 434782608695652173913*23
9999999999999999999999

julia> 1.0/14
0.07142857142857142

julia> 714285714285*14
9999999999990

julia> 714285*14
9999990
```