Respuesta :
Answer:
x = 22.
Step-by-step explanation:
6x ≡ 7(mod 25)
6x ≡ 25n + 7 where x and n are integers.
Checking multiples of 25:
25: (n= 1) 25+7 = 32. 6*5 = 2 (mod 25) . Does not fit.
50, 75 , 100 do not fit either.
The answer is 22 because 6*22 = 132 = 125 + 7 = 7(mod 25).
The solution to the congruence equation 6x ≡ 7(mod 25) is x = 22.
We have the congruence equation
6x ≡ 7(mod 25)
6x ≡ 25n + 7 where x and n are integers.
So, it means 25 divides 6x-7.
As 25 divides 6x-7 . So value of x should be greater than 5.
It does not work for 6,7,..... 21.
For x=22
[tex]6*22 = 132 \\= 125 + 7 \\= 7(mod 25).[/tex]
The solution for the congruence equation 6x ≡ 7(mod 25) is x=22.
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