To determine: The smallest nonnegative integer x that satisfies the given system of congruences. x\equiv 3\pmod 5 x\equiv 7\pmod 8

Wribreeminsl

Wribreeminsl

Answered question

2021-04-16

To determine: The smallest nonnegative integer x that satisfies the given system of congruences.
x3±od5
x7±od8

Answer & Explanation

Theodore Schwartz

Theodore Schwartz

Skilled2021-04-18Added 99 answers

x3±od5
x7±od8
We see that the solution x is unique modulo 5.8=40.
Now, 8(2)-5(3)=1.
Thus,
x=3.8(2)-7.5(3)
x=48-105
x=-57
x=17±od{40}
x=23±od{40}
Therefore, x =23.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school geometry

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?