Determine the greatest common divisor of the elements of the set \[ s = \{ n^{13} - n \mid n \in \mathbb{z} \}. \]

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.

b.) 160 miles on a 5 gallons car

step-by-step explanation:

240/10=24 miles/gallon

160/5=32 miles/gallon

30/1=30 miles/gallon

168/6= 28 miles/gallon

32 miles/gallon is the most amount, so this is the best.