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x = 14k+11 where k = 0, 1, 2, ...
but what would the reduced form be?
reduced form? i think that's the simplest way to express x
i mean the original equation is 11 mod 7 so could i not write that as 4 mod 7
x = 11 mod 7 is equivalent to x = 4 mod 7 and x=7k+4 k = 0, 1, 2, ...
where did the 14 come in?
because the original problem was to find the smallest specific solution for x=1 (mod 2) and x=4 (mod 7)
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)
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.
18 = 4 mod 14 but 18 = 0 mod 2
so i should just leave it as x=11 (mod 7) right
i mean x= 11 mod 14
wolfram alpha says 1(mod 2) =11 (mod 14) is false
it should be a solution but its not working
@wednesday09876 you said that the original problem is x=1 (mod 2) x =4 (mod 7) Q: find the smallest number of x?
Question: Give the smallest specific solution and the modulus for its congruence class.
x = 11. that is the smallest number that satisfies x = 1 mod 2 and x = 4 mod 7
okay. so my final answer is going to be x=11 (mod 14) right?
1 mod 2 <> 11 mod 14... only = in certain cases.
if they want the smallest number, it's 11. if they want all numbers then it's x = 11 mod 14,