Tìm số tự nhiên a nhỏ nhất thỏa mãn

Để tìm số tự nhiên a nhỏ nhất thỏa mãn yêu cầu đề bài, ta cần tìm số tự nhiên a sao cho:
- a ≡ 4 (mod 7)
- a ≡ 6 (mod 11)
- a ≡ 9 (mod 17)

Ta sẽ giải hệ phương trình đồng dư trên bằng phương pháp ngược và sử dụng định lý nhỏ Fermat.

Đầu tiên, ta có:
- 7 ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod 6) => 7^(-1) ≡ 1 (mod