math from FIL

根據題目分析，先按照餘數分類：
假設答案為 N
mod 1,3,7,9 餘 0 ........ (1)
mod 2,4,5,8 餘 1 ........ (2)
mod 6 餘 3 .............. (3)

lcm(3,7,9) = 63 ......... (4), by (1)
lcm(2,4,5,8) = 40 ....... (5), by (2)

N ≡ 0 mod 63 ..... (6), by (4)
N ≡ 1 mod 40 ..... (7), by (5)
N ≡ 3 mod 6 ....... (8), by (3)

Solve integer m,n,l
N = 63m ........... (9), by (6)
  = 40n + 1 ....... (10), by (7)
  = 6l + 3 ........ (11), by (8)

63m = 60m + 3m = 6l + 3 ....... by (6),(8)
3m ≡ 3 mod 6
3m = 3(2s+1) = 6s + 3 ≡ 3 mod 6
m = 2s + 1 ........ (12)

63m = 63(2s+1)
    = 126s + 63
    = 40(3s+1) + 6s + 23  ≡ 1 mod 40
6s + 23  ≡ 1 mod 40
6s + 23 = 40p + 1 ....... (13)

By brute force:
Given p = 1:
s = 3 ....... by (13)
m = 7 ....... by (12)
N = 63 * 7... by (6)
  = 441