Question

Part #1: Prove or disprove (formally or informally): The sum of an integer and its cube...

Part #1:

Prove or disprove (formally or informally): The sum of an integer and its cube is even.

Part #2:

Provide counterexamples to the following statements.

If n2 > 0 then n > 0.

If n is an even number, then n2 + 1 is prime.

(n2 is n to the power of 2).

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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.
(a) Prove or disprove the statement (where n is an integer): If 3n + 2 is...
(a) Prove or disprove the statement (where n is an integer): If 3n + 2 is even, then n is even. (b) Prove or disprove the statement: For irrational numbers x and y, the product xy is irrational.
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.
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...
Prove or disprove the following statement: 2^(n+k) is an element of O(2^n) for all constant integer...
Prove or disprove the following statement: 2^(n+k) is an element of O(2^n) for all constant integer values of k>0.
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 ∈...
(§2.1) Let a,b,p,n ∈Z with n > 1. (a) Prove or disprove: If ab ≡ 0...
(§2.1) Let a,b,p,n ∈Z with n > 1. (a) Prove or disprove: If ab ≡ 0 (mod n), then a ≡ 0 (mod n) or b ≡ 0 (mod n). (b) Prove or disprove: Suppose p is a positive prime. If ab ≡ 0 (mod p), then a ≡ 0 (mod p) or b ≡ 0 (mod p).
Show 2 different solutions to the task. Prove that for every integer n (...-3, -2, -1,...
Show 2 different solutions to the task. Prove that for every integer n (...-3, -2, -1, 0, 1, 2, 3, 4...), the expression n2 + n will always be even.
Prove or disprove the following statements. Remember to disprove a statement you have to show that...
Prove or disprove the following statements. Remember to disprove a statement you have to show that the statement is false. Equivalently, you can prove that the negation of the statement is true. Clearly state it, if a statement is True or False. In your proof, you can use ”obvious facts” and simple theorems that we have proved previously in lecture. (a) For all real numbers x and y, “if x and y are irrational, then x+y is irrational”. (b) For...
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.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT