Find integer that satisfies two congruences Find the integer between $0$ and $29\times 23$ $= 667$ that satisfies the two following congruences: 
$x ≡ 15$ (mod $23$)
$x ≡ 1$ (mod $29$).

$29 = 6\pmod{23}\\
6\cdot 4 = 1\pmod{23}\\
1+2\cdot 6+2\cdot 1 = 15\\
1+2\cdot29 + 8\cdot 29 \equiv 15\pmod{23}$
291
