Question

2. Steve claims that two even numbers can never be relatively prime. Explain why his
claim is true.​

Answer 1

Answer:

I think you are talking about a ( Primality tests), this is a different issue.

In fact, there are hundreds of formulas that test numbers if they are prime or not. For example:

(1) n is prime if and only if [(n-1)! +1]/n is an integer number.

(2)If (2n-1 -1)/n is not an integer, then n is a composite number.

(3) n is prime if and only if all coefficients of the polynomial

[(x+y)n - xn - yn ]/xy(x+y) are divisible by n.

(4) Miller - Rabin test

(5) Elliptic curve primality test.

(6) AKS primality test.

(7) Fermat's test

(8) Lucas Lehmer test.

And many more.

The advantage of each test is given by its complexity ).

( The time needed to perform the test)

Hope your algorithm has good complexity.

Best regards

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:When two numbers have no common factors other than 1.

In other words there is no value that you could divide them both by exactly (without any remainder).

21 and 22 are relatively prime:

• The factors of 21 are 1, 3, 7 and 21

• The factors of 22 are 1, 2, 11 and 22

(the only common factor is 1)

But 21 and 24 are NOT relatively prime:

• The factors of 21 are 1, 3, 7 and 21

• The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24

(the common factors are 1 AND 3)

Relatively Prime is also called "coprime" or "mutually prime".

Here we see that 12 and 16 are NOT relatively prime

See: Factor

Relatively Prime