Question

Let x ∈ N. Prove that if (x + 3)^2 is prime, then x^3 − x...

Let x ∈ N. Prove that if (x + 3)^2 is prime, then x^3 − x − 2020 ≤ 0

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

Homework Answers

Answer #1

For , is a divisor of .

If   is prime then only divisor of is 1 or itself .

Now as   is a divisor of

or  

or ,  

or   

a contradiction to   .

So there is no such and hence satisfies vacously .

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
3.a) Let n be an integer. Prove that if n is odd, then (n^2) is also...
3.a) Let n be an integer. Prove that if n is odd, then (n^2) is also odd. 3.b) Let x and y be integers. Prove that if x is even and y is divisible by 3, then the product xy is divisible by 6. 3.c) Let a and b be real numbers. Prove that if 0 < b < a, then (a^2) − ab > 0.
Let n be an integer, with n ≥ 2. Prove by contradiction that if n is...
Let n be an integer, with n ≥ 2. Prove by contradiction that if n is not a prime number, then n is divisible by an integer x with 1 < x ≤√n. [Note: An integer m is divisible by another integer n if there exists a third integer k such that m = nk. This is just a formal way of saying that m is divisible by n if m n is an integer.]
3. Prove by contrapositive: Let n ∈ N. If n^3−5n−10>0,then n ≥ 3. 4. Prove: Letx∈Z....
3. Prove by contrapositive: Let n ∈ N. If n^3−5n−10>0,then n ≥ 3. 4. Prove: Letx∈Z. Then5x−11 is even if and only if x is odd. 4. Prove: Letx∈Z. Then 5x−11 is even if and only if x is odd.
Let p be an odd prime, and let x = [(p−1)/2]!. Prove that x^2 ≡ (−1)^(p+1)/2...
Let p be an odd prime, and let x = [(p−1)/2]!. Prove that x^2 ≡ (−1)^(p+1)/2 (mod p). (You will need Wilson’s theorem, (p−1)! ≡−1 (mod p).) This gives another proof that if p ≡ 1 (mod 4), then x^2 ≡ −1 (mod p) has a solution.
Let h € N be a prime. Now prove for all b € N, h divides...
Let h € N be a prime. Now prove for all b € N, h divides b^h -b.
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?)
Let f ∈ Z[x] be a nonconstant polynomial. Prove that the set S = {p prime:...
Let f ∈ Z[x] be a nonconstant polynomial. Prove that the set S = {p prime: there exist infinitely many positive integers n such that p | f(n)} is infinite.
Prove the following statements: 1- If m and n are relatively prime, then for any x...
Prove the following statements: 1- If m and n are relatively prime, then for any x belongs, Z there are integers a; b such that x = am + bn 2- For every n belongs N, the number (n^3 + 2) is not divisible by 4.
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)!.
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 ∈...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT