Question

If 3x= 5(mod7) , then

a) x= 2(mod7)
b) x= 3(mod7)
c) x= 4(mod7)​

Answer 1

Answer:

c)x=4(mod7)

Step-by-step explanation:

In arithmetic modulo 7 , a multiplicative inverse of 3 is 5. This result can be obtained by writing a modulo- 7 times table for 3 until you get the product 1.

Then multiply the given congruence by 5 to get x by itself:

5×3x≡5×5 (mod 7)

and this means that the left-hand side of the congruence is

5×3x≡1x≡x(mod 7).

Then x≡25≡4+3×7

≡4+3×0≡4 (mod 7)

is a solution to the congruence.

All solutions to the given congruence have the form x=4+7t where t is an integer.