To find the remainder when 2n is divided by 6, we can use the information given.

We know that when n is divided by 6, the remainder is 4. This can be written as n ≡ 4 (mod 6), where "≡" denotes congruence.

To find the remainder when 2n is divided by 6, we can multiply both sides of the congruence by 2:

2n ≡ 2 * 4 (mod 6)

Simplifying, we get:

2n ≡ 8 (mod 6)

Now, we need to find an equivalent congruence where the remainder is between 0 and 5.

Since 8 divided by 6 gives a remainder of 2, we can write:

2n ≡ 2 (mod 6)

Therefore, when 2n is divided by 6, the remainder is 2.

Question

To find the remainder when 2n is divided by 6, we can use the information given.

We know that when n is divided by 6, the remainder is 4. This can be written as n ≡ 4 (mod 6), where "≡" denotes congruence.

To find the remainder when 2n is divided by 6, we can multiply both sides of the congruence by 2:

2n ≡ 2 * 4 (mod 6)

Simplifying, we get:

2n ≡ 8 (mod 6)

Now, we need to find an equivalent congruence where the remainder is between 0 and 5.

Since 8 divided by 6 gives a remainder of 2, we can write:

2n ≡ 2 (mod 6)

Therefore, when 2n is divided by 6, the remainder is 2.

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