Question

Recall that ν(n) is the divisor function: it gives the number of positive divisors of n....

Recall that ν(n) is the divisor function: it gives the number of positive divisors of n. Prove that ν(n) is a prime number if and only if n = pq-1 , where p and q are prime numbers.

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
An integer 'n' greater than 1 is prime if its only positive divisor is 1 or...
An integer 'n' greater than 1 is prime if its only positive divisor is 1 or itself. For example, 2, 3, 5, and 7 are prime numbers, but 4, 6, 8, and 9 are not. Write a python program that defines a function isPrime (number) with the following header: def isPrime (number): that checks whether a number is prime or not. Use that function in your main program to count the number of prime numbers that are less than 5000....
Let m,n be any positive integers. Show that if m,n have no common prime divisor (i.e....
Let m,n be any positive integers. Show that if m,n have no common prime divisor (i.e. a divisor that is at the same time a prime number), then m+n and m have no common prime divisor. (Hint: try it indirectly)
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...
Assume that p does not divide n for every prime number p with n> 1 and...
Assume that p does not divide n for every prime number p with n> 1 and p <= (n) ^ (1/3). Then prove that n is a prime number or a product of two prime numbers
8. Prove or disprove the following statements about primes: (a) (3 Pts.) The sum of two...
8. Prove or disprove the following statements about primes: (a) (3 Pts.) The sum of two primes is a prime number. (b) (3 Pts.) If p and q are prime numbers both greater than 2, then pq + 17 is a composite number. (c) (3 Pts.) For every n, the number n2 ? n + 17 is always prime.
For C++: a) Write a function is_prime that takes a positive integer X and returns 1...
For C++: a) Write a function is_prime that takes a positive integer X and returns 1 if X is a prime number, or 1 if X is not a prime number. b) write a program that takes a positive integer N and prints all prime numbers from 2 to N by calling your function is_prime from part a.
Let a positive integer n be called a super exponential number if its prime factorization contains...
Let a positive integer n be called a super exponential number if its prime factorization contains at least one prime to a power of 1000 or larger. Prove or disprove the following statement: There exist two consecutive super exponential numbers.
The greatest common divisor c, of a and b, denoted as c = gcd(a, b), is...
The greatest common divisor c, of a and b, denoted as c = gcd(a, b), is the largest number that divides both a and b. One way to write c is as a linear combination of a and b. Then c is the smallest natural number such that c = ax+by for x, y ∈ N. We say that a and b are relatively prime iff gcd(a, b) = 1. Prove that a and n are relatively prime if and...
In number theory, Wilson’s theorem states that a natural number n > 1 is prime if...
In number theory, Wilson’s theorem states that a natural number n > 1 is prime if and only if (n − 1)! ≡ −1 (mod n). (a) Check that 5 is a prime number using Wilson’s theorem. (b) Let n and m be natural numbers such that m divides n. Prove the following statement “For any integer a, if a ≡ −1 (mod n), then a ≡ −1 (mod m).” You may need this fact in doing (c). (c) The...
python If a number num1 divides another number num2 evenly then num1 is a divisor of...
python If a number num1 divides another number num2 evenly then num1 is a divisor of num2. For example, 2 is a divisor of 2, 4, 6, 8, but 2 is not a divisor of 1, 3, 5, 7, 9, 11, 13. Write a function named count_divisors(m,n) that works as follows. Input: the function takes two integer arguments m and n Process: the function asks the user to enter numbers (positive or negative), and counts the total number of inputs...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT