Question

Find all positive integers n such that n^4- 1 is divisible by 5.​

Answer 1

Answer:

All positive integers except multiple of 5.

Step-by-step explanation:

From the rule of divisibility, a number's last digit should be either 0 or 5 for it to be divisible by 5.

For $(n^{4} - 1)$ to be a multiple of 5, the last digit of $(n^{4} - 1)$ should be 0 or 5. In other words, the last digit of $n^{4}$ should be 1 or 6.

The last digit of $n^{4}$ is 1 if $n$ is an odd number except those that are multiples of 5.

The last digit of $n^{4}$ is 6 if $n$ is an even number except those that are multiples of 5.

Therefore, the possible values of $n$ are all positive integers except those that are multiples of 5.