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aksik [14]
3 years ago
12

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

Mathematics
1 answer:
zzz [600]3 years ago
5 0

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.

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