# To determine: The smallest nonnegative integer x that satisfies the given system of congruences. x\equiv 1003\pmod {17,369} x\equiv 2974\pmod {5472}

Isa Trevino 2021-03-25 Answered
To determine: The smallest nonnegative integer x that satisfies the given system of congruences.
$x\equiv 1003±od\left\{17,369\right\}$
$x\equiv 2974±od\left\{5472\right\}$
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## Expert Answer

ottcomn
Answered 2021-03-27 Author has 97 answers
$x\equiv 1003±od\left\{17,369\right\}$
$x\equiv 2974±od\left\{5472\right\}$
We see that the solution x is unique modulo 17369.5472=95043168.
Now, 17369(-2647)-5472(8402)=1.
Thus,
x=2974.17369(-2647)-1003.5472(8402)
x=46113671232-136731859682
x=-90618188450
$x=-52992822±od\left\{950431168\right\}$
Therefore, x=-52992822.
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