Question

State whether the following statements are false or true, explain your answer:
7x ≡ 12(mod 7).​

Answer 1

False the above statement is false

Answer 2

Given :  7x ≡ 12(mod 7).​

To Find :  false or true

Solution:

ax ≡ b (mod n)

has at least one solution if

HCF ( a , n)   is a divisor of b  

7x ≡ 12(mod 7)

a = 7

b = 12

n = 7

HCF ( 7  , 7)  = 7

7 is not a divisor of 12

Hence there is no solution

so   7x ≡ 12(mod 7) is FALSE

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