Question

what is x= 11 (Mod 14)?

Answer 1

x = 14k+11 where k = 0, 1, 2, ...

Answer 2

but what would the reduced form be?

Answer 3

reduced form? i think that's the simplest way to express x

Answer 4

i mean the original equation is 11 mod 7 so could i not write that as 4 mod 7

Answer 5

x = 11 mod 7 is equivalent to x = 4 mod 7 and x=7k+4 k = 0, 1, 2, ...

Answer 6

where did the 14 come in?

Answer 7

because the original problem was to find the smallest specific solution for
x=1 (mod 2)
and
x=4 (mod 7)

Answer 8

ok...

Answer 9

so what im gonna do is reduce x= 11 (mod 7) into x =4 (mod 7) and then just make it x=4 (mod 14)

Answer 10

no... tha won't satisfy the original. think about it... whatever x is, it has to be odd. otherwise, x = 0 mod 2.
therefore, it would be x = 7k + 4, k = 1, 3, 5, ... or the other way to write it would be
x = 14n + 11, n = 0, 1, 2, ...
you'll see you get the same numbers... k = 1 is the same as n = 0, k = 3 is the same as n = 1, and so on.

Answer 11

18 = 4 mod 14 but 18 = 0 mod 2

Answer 12

so i should just leave it as x=11 (mod 7) right

Answer 13

i mean x= 11 mod 14

Answer 14

yeah

Answer 15

wolfram alpha says 1(mod 2) =11 (mod 14) is false

Answer 16

it should be a solution but its not working

Answer 17

@wednesday09876 you said that the original problem is
x=1 (mod 2)
x =4 (mod 7)
Q: find the smallest number of x?

Answer 18

Question: Give the smallest specific solution and the modulus for its congruence class.

Answer 19

x = 11. that is the smallest number that satisfies

x = 1 mod 2 and x = 4 mod 7

Answer 20

okay. so my final answer is going to be x=11 (mod 14) right?

Answer 21

1 mod 2 <> 11 mod 14... only = in certain cases.

Answer 22

if they want the smallest number, it's 11. if they want all numbers then it's x = 11 mod 14,

Answer 23

great thanks.

Answer 24

you're welcome