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3 votes
How many three-digit positive integers
x satisfy
3874x+481\equiv 1205 \pmod{23}

User IgalSt
by
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1 Answer

3 votes

Answer:

40

Explanation:

Any solution x will mod 23 will also have x+23n as a solution, for some integer n. Since 900/23 = 39 3/23, we know there are 39 or 40 three-digit integers of this form.

As it happens, 100 is the smallest 3-digit solution. So, there are 40 three-digit numbers that are of the form 100 +23n, hence 40 solutions to the equation.

_____

The equation reduces, mod 23, to ...

10x = 11

Its solutions are x = 23n +8.

User Liberty
by
8.1k points