Respuesta :
A) Find a number [tex]0\leq x<14[/tex] that solves the congruence [tex]9x \equiv 9 \pmod{14}[/tex].
[tex]9x \equiv 9 \pmod{14}[/tex] means that 9x-9 is a multiple of 14,
that is 9(x-1) is a multiple of 14. A clear solution in the set is x=1
b) Find a number [tex]0\leq x<5[/tex] that solves the congruence [tex]3x \equiv 4 \pmod{5}[/tex].
[tex]3x \equiv 4 \pmod{5}[/tex] means that 3x-4 is a multiple of 5,
x∈{0, 1, 2, 3, 4} , so for these values 3x-4 becomes {-4, -1, 2, 5, 8}.
so x= 3
c)Find a number [tex]0\leq x<1000[/tex] that solves the congruence [tex]999x \equiv 998 \pmod{1000}[/tex].
[tex]999x \equiv 998 \pmod{1000}[/tex] means that 999x-998 is a multiple of 1,000
we can check that for x=2, 999*2-998=1,998-998=1,000
d)Find a number [tex]0\leq x<21[/tex] that solves the congruence [tex]4x \equiv 17 \pmod{21}[/tex]
[tex]4x \equiv 17 \pmod{21}[/tex] 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
