To determine: The smallest nonnegative integer x that satisfies the given system of congruences.x\equiv 3\pmod 5x\equiv 3\pmod 7

EunoR 2021-02-18 Answered

To determine: The smallest nonnegative integer x that satisfies the given system of congruences.
x3±5
x3±7

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Expert Answer

Derrick
Answered 2021-02-20 Author has 94 answers

x3±5
x3±7
We see that the solution x is unique modulo 7.5=35
Now, 5(10)-7(7)=1.
Thus,
x=4.5(10)-3.7(7)
x=200-147
x=53
x=18±35
Therefore, x = 18.

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