Find all integers x, and odd integers n such that, 1 + n^2 = x^3. Please...

Question

Question

Find all integers x, and odd integers n such that, 1 + n^2 = x^3. Please give an explanation with proof thank you.

Answer 1

Answer #1

solution. satisfy Let n be an odd integer 1+ n²x - To Find all xE71 {set of integest} andn. It (2k + 1)² = x² ( n= akt I his

Answer 2

Similar Homework Help Questions

Problem 2. Find (with proof) all positive integers n that have an odd number of positive...

Problem 2. Find (with proof) all positive integers n that have an odd number of positive divisors (for example 6 has 4 positive divisors 1,2,3,6).
please help me with this question: 19. Give a story proof that 72 +3 for all integers n 2 2. Hint: Consider the middle number in a subset of (1,2.,n +3) of size 5. 19. Give a story proof that 72...

please help me with this question: 19. Give a story proof that 72 +3 for all integers n 2 2. Hint: Consider the middle number in a subset of (1,2.,n +3) of size 5. 19. Give a story proof that 72 +3 for all integers n 2 2. Hint: Consider the middle number in a subset of (1,2.,n +3) of size 5.
Please answer all!! 3. Show that if n e Z so that n is odd then...

Please answer all!! 3. Show that if n e Z so that n is odd then 8|n2 + (n + 6)2 +6. 4. (a) Let a, b, and n be integers so that n > 2. Define: а is congruent to b mod n. The notation here is a = b (modn). (b) Is 12 = 4 (mod 2)? Explain. (c) Is 25 = 3 (mod 2)? Explain. (d) Is 27 = 13 (mod8)? Explain. (e) Find 6 integers x...

3- A signal to, is odd if x.(n) = -2.(-n). Show that for such a signal,...

3- A signal to, is odd if x.(n) = -2.(-n). Show that for such a signal, we have x,0) = 0. Give an example of an odd signal.
please answer questions #7-13 7. Use a direct proof to show every odd integer is the...

please answer questions #7-13 7. Use a direct proof to show every odd integer is the difference of two squares. [Hint: Find the difference of squares ofk+1 and k where k is a positive integer. Prove or disprove that the products of two irrational numbers is irrational. Use proof by contraposition to show that ifx ty 22 where x and y are real numbers then x 21ory 21 8. 9. 10. Prove that if n is an integer and 3n...
3) [3 marks] Use a proof by cases that for all real number x, xs]x]. You...

3) [3 marks] Use a proof by cases that for all real number x, xs]x]. You may need this definition. For any real numbers x, [x]= x, if x2 0, -x, otherwise. 4) [3 marks] Give a direct proof that If x is an odd integer and y is an even integer, then x + y is odd. 5) [3 marks] Give a proof by contradiction for the proposition in Q4, above. That is, give a proof by contraction for...

Find all integers x, y, 0 < x, y < n, that satisfy each of the...

Find all integers x, y, 0 < x, y < n, that satisfy each of the following pairs of congruences. If no solutions exist, explain why. (a) x + 5y = 3(mod n), and 4x + y = 1(mod n), for n = 8. (b) 7x + 2y = 3(mod n), and 9x + 4y = 6(mod n), for n=5.
(2) x + 1 is even -> x^2 is odd (hint: use a direct proof) (a)...

(2) x + 1 is even -> x^2 is odd (hint: use a direct proof) (a) (0.5 points) What are you assuming is true: (b) (0.5 points) What are you proving is true: (c) (1 point) Complete the proof:
answer all parts please 1. (12 points) Prove that if n is an integer, then na...

answer all parts please 1. (12 points) Prove that if n is an integer, then na +n + 1 is odd. 2. (12 points) Prove that if a, b, c are integers, c divides a +b, and ged(a,b) -1, then god (ac) - 1. 3. (a) (6 points) Use the Euclidean Algorithm to find ged(270, 105). Be sure to show all the steps of the Euclidean algorithm and, once you have finished the Euclidean Algorithm, to finish the problem by...

Assignment 6 1. Prove by contradiction that: there are no integers a and b for which...

Assignment 6 1. Prove by contradiction that: there are no integers a and b for which 18a+6b = 1. 2. Prove by contradiction that: if a,b ∈ Z, then a2 −4b ≠ 2 3. Prove by contrapositive that: If x and y are two integers whose product is even, then at least one of the two must be even. Make sure that you clearly state the contrapositive of the above statement at the beginning of your proof. 4. Prove that...