Question

Find the least positive integer with remainders 1, 2, and 3 when divided by 7, 8, and 9 respectively.

Answer 1

\[x \equiv 1 (\mod 7)\]

Answer 2

\[x \equiv 2 (\mod 8)\]
\[x \equiv 9 (\mod 9) \]

Answer 3

\[x =f_1+2f_2+3f_3 \mod 7 \]
\[x =f_1+2f_2+3f_3 \mod 8\]
\[x =f_1+2f_2+3f_3 \mod 9 \]

Answer 4

\[f_1 = 8 \times 9 \times b_1 \mod 7\]
\[f_2 = 7 \times 9 \times b_1 \mod 8\]
\[f_3 = 7 \times 8 \times b_3 \mod 9\]

Answer 5

\[f_1 = 72 \times b_1 \mod 7\]
\[f_2 = 63 \times b_2 \mod 8\]
\[f_3 = 56 \times b_1 \mod 9\]