# To determine: The smallest nonnegative integer x that satisfies the given system of congruences. x\equiv 1\pmod 4 x\equiv 8\pmod 9

To determine: The smallest nonnegative integer x that satisfies the given system of congruences.
$x\equiv 1±od4$
$x\equiv 8±od9$
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falhiblesw
$x\equiv 1±od4$
$x\equiv 8±od9$
We see that the solution x is unique modulo 9.4=36.
Now, 9(1)-4(2)=1.
Thus,
x=1.9(1)-8.4(2)
x=9-64
x=-55
$x=-19±od\left\{36\right\}$
$x=17±od\left\{36\right\}$
Therefore, x=17.