To determine: The smallest nonnegative integer x that satisfies the given system of congruences. x\equiv 3\pmod {1917} x\equiv 75\pmod {385}

Trent Carpenter

Trent Carpenter

Answered question

2021-05-04

To determine: The smallest nonnegative integer x that satisfies the given system of congruences.
x3±od{1917}
x75±od{385}

Answer & Explanation

Nicole Conner

Nicole Conner

Skilled2021-05-06Added 97 answers

x3±od{1917}
x75±od{385}
We see that the solution x is unique modulo 385.1917=738045.
Now, 1917(48)-385(239)=1.
Thus,
x=75.1917(48)-3.385(239)
x=6901200-276045
x=6625155
x=720795±od{738045}
Therefore, x = 720795.

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