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artcher [175]
3 years ago
9

A) Find a number $0\leq x<14$ that solves the congruence $9x \equiv 9 \pmod{14}$.

Mathematics
1 answer:
Rus_ich [418]3 years ago
6 0
 

A) Find a number 0\leq x that solves the congruence 9x \equiv 9 \pmod{14}<span>.

</span>9x \equiv 9 \pmod{14} means that 9x-9 is a multiple of 14, 
<span>
that is 9(x-1) is a multiple of 14. A clear solution in the set is x=1



b) Find a number </span>0\leq x that solves the congruence 3x \equiv 4 \pmod{5}<span>.


</span>3x \equiv 4 \pmod{5} means that 3x-4 is a multiple of 5, 
<span>
x</span>∈{0, 1, 2, 3, 4} , so for these values 3x-4 becomes {-4, -1, 2, 5, 8}.

so x= 3 <span>


c)Find a number </span>0\leq x that solves the congruence 999x \equiv 998 \pmod{1000}<span>.


</span>999x \equiv 998 \pmod{1000} means that 999x-998 is a multiple of 1,000<span>

we can check that for x=2,         999*2-998=1,998-998=1,000


d)Find a number </span>0\leq x that solves the congruence 4x \equiv 17 \pmod{21}

4x \equiv 17 \pmod{21} means that 4x-17 is a multiple of 21, 

fro x=7, 4x=28 and so 4x-17=28-17=21 is a multiple of 21.



Answers:

A) 1
B) 3
C) 2
D) 4
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