# To determine: The smallest nonnegative integer x that satisfies the given system of congruences. x\equiv 6\pmod 8 x\equiv 17\pmod {25}

To determine: The smallest nonnegative integer x that satisfies the given system of congruences.
$x\equiv 6±od8$
$x\equiv 17±od\left\{25\right\}$
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hajavaF
$x\equiv 6±od8$
$x\equiv 17±od\left\{25\right\}$
We see that the solution x is unique modulo 25.8=200.
Now, 25(1)-8(3)=1.
Thus,
x=6.25(1)-17.8(3)
x=150-408
x=-258
$x=-58±od\left\{200\right\}$
$x=142±od\left\{40\right\}$
Therefore, x=142.