When 3n is divided by 7 the remainder is 4. What is the remainder when when 2n is divided by 7?
(With solution pls...) tnx
To find the remainder when 2n is divided by 7, we can first analyze the given information.
We are told that when 3n is divided by 7, the remainder is 4. This can be represented as:
3n ≡ 4 (mod 7)
Here, "≡" represents congruence, meaning that 3n is congruent to 4 modulo 7.
To find the remainder when 2n is divided by 7, we need to express 2n in terms of 3n using the given congruence. Let's manipulate the equation we derived earlier:
3n ≡ 4 (mod 7)
Multiply both sides of the congruence by 2:
6n ≡ 8 (mod 7)
Now, let's reduce the right-hand side of the congruence:
6n ≡ 1 (mod 7)
We can conclude that 2n is congruent to 1 modulo 7:
2n ≡ 1 (mod 7)
This means that the remainder when 2n is divided by 7 is 1.