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.
x1003±od{17,369}
x2974±od{5472}
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ottcomn
Answered 2021-03-27 Author has 97 answers
x1003±od{17,369}
x2974±od{5472}
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{950431168}
Therefore, x=-52992822.
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