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 [tex](n^{4} - 1)[/tex] to be a multiple of 5, the last digit of [tex](n^{4} - 1)[/tex] should be 0 or 5. In other words, the last digit of [tex]n^{4} [/tex] should be 1 or 6.
The last digit of [tex]n^{4}[/tex] is 1 if [tex]n[/tex] is an odd number except those that are multiples of 5.
The last digit of [tex]n^{4}[/tex] is 6 if [tex]n[/tex] is an even number except those that are multiples of 5.
Therefore, the possible values of [tex]n[/tex] are all positive integers except those that are multiples of 5.
