Determine the greatest common divisor of the elements of the set \[ s = \{ n^{13} - n \mid n \in \mathbb{z} \}. \]
1 answer:
Answer:
2730
Step-by-step explanation:
We want to determine the greatest common divisor of the elements of the set
We apply the Fermat's little theorem which states that if p is a prime number, then for any integer a, the number aᵖ − a is an integer multiple of p.
Now, if p-1 divides 12.
Since the of 12 are 1,2,3,4, 6, 12, the corresponding primes are 2, 3, 5, 7, 13.
Therefore, the gcd of the elements in and
2*3*5*7*13=2730
Therefore, the gcd of the elements in set S is 2730.
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