Question

Let x be an integer bigger than 4. Prove that x is prime if and only...

Let x be an integer bigger than 4. Prove that x is prime if and only if x does not divide (x − 1)!.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
4. Prove that if p is a prime number greater than 3, then p is of...
4. Prove that if p is a prime number greater than 3, then p is of the form 3k + 1 or 3k + 2. 5. Prove that if p is a prime number, then n √p is irrational for every integer n ≥ 2. 6. Prove or disprove that 3 is the only prime number of the form n2 −1. 7. Prove that if a is a positive integer of the form 3n+2, then at least one prime divisor...
Problem 2: (i) Let a be an integer. Prove that 2|a if and only if 2|a3....
Problem 2: (i) Let a be an integer. Prove that 2|a if and only if 2|a3. (ii) Prove that 3√2 (cube root) is irrational. Problem 3: Let p and q be prime numbers. (i) Prove by contradiction that if p+q is prime, then p = 2 or q = 2 (ii) Prove using the method of subsection 2.2.3 in our book that if p+q is prime, then p = 2 or q = 2 Proposition 2.2.3. For all n ∈...
4) Let F be a finite field. Prove that there exists an integer n ≥ 1,...
4) Let F be a finite field. Prove that there exists an integer n ≥ 1, such that n.1F = 0F . Show further that the smallest positive integer with this property is a prime number.
Let a be prime and b be a positive integer. Prove/disprove, that if a divides b^2...
Let a be prime and b be a positive integer. Prove/disprove, that if a divides b^2 then a divides b.
Let p be an odd prime and let a be an odd integer with p not...
Let p be an odd prime and let a be an odd integer with p not divisible by a. Suppose that p = 4a + n2 for some integer n. Prove that the Legendre symbol (a/p) equals 1.
Formal Proof: Let p be a prime and let a be an integer. Assume p ∤...
Formal Proof: Let p be a prime and let a be an integer. Assume p ∤ a. Prove gcd(a, p) = 1.
1)Let ? be an integer. Prove that ?^2 is even if and only if ? is...
1)Let ? be an integer. Prove that ?^2 is even if and only if ? is even. (hint: to prove that ?⇔? is true, you may instead prove ?: ?⇒? and ?: ? ⇒ ? are true.) 2) Determine the truth value for each of the following statements where x and y are integers. State why it is true or false. ∃x ∀y x+y is odd.
Let p be a prime that is congruent to 3 mod 4. Prove that there is...
Let p be a prime that is congruent to 3 mod 4. Prove that there is no solution to the congruence x2≡−1 modp. (Hint: what would be the order of x?)
1. Let n be an integer. Prove that n2 + 4n is odd if and only...
1. Let n be an integer. Prove that n2 + 4n is odd if and only if n is odd? PROVE 2. Use a table to express the value of the Boolean function x(z + yz).
A prime number (or a prime) is an integer greater than 1 that is not a...
A prime number (or a prime) is an integer greater than 1 that is not a product of two smaller integer. Created a program on visual studio named PrimeNumberTest that does the following: 1) prompt the user for input of an integer 2) test if the integer is a prime number 3) display the test result