prove that there exist infinitely many primitive Pythagorean triples

Expert Solution

Colby Messinger answered 1 year ago

Prove that there exist infinitely many positive real numbers r such that the equation 2x +...

Prove that there exist infinitely many positive real numbers r such that the equation 2x + 3y + 5z = r has no solution (x,y,z) ∈ Q × Q × Q. (Hint: Is the set S = {2x + 3y + 5z : (x,y,z) ∈ Q × Q × Q} countable?)

If (x,y,z) is a primitive Pythagorean triple, prove that z= 4k+1

Let x, y, z be a primitive Pythagorean triple with y even. Prove that x+y ≡...

Let x, y, z be a primitive Pythagorean triple with y even. Prove that x+y ≡ x−y ≡ ±1 mod 8.

Prove that the union of infinitely many countable sets is countable.

How can we use Hilbert's theorem 90 to find all Pythagorean triples?

Prove: There are infinitely many primes of the form 6n − 1 (n is an integer).

Discrete math problem: Prove that there are infinitely many primes of form 4n+3.

Show that if (x,y,z) is a primitive Pythagorean triple, then X and Y cannot both be...

Show that if (x,y,z) is a primitive Pythagorean triple, then X and Y cannot both be even and cannot both be odd. Hint: for the odd case, assume that there exists a primitive Pythagorean triple with X and Y both odd. Then use the proposition "A perfect square always leaves a remainder r=0 or r=1 when divided by 4." to produce a contradiction.

Prove this is true: The sequence {4k + 3} where k ∈ N contains infinitely many...

Prove this is true: The sequence {4k + 3} where k ∈ N contains infinitely many primes, but the sequence {4k + 2} does not.

Prove this is true: The sequence {4k + 3} where k ∈ N contains infinitely many...

Prove this is true: The sequence {4k + 3} where k ∈ N contains infinitely many primes, but the sequence {4k + 2} does not. Show your work.

Question

prove that there exist infinitely many primitive Pythagorean triples

Solutions

Expert Solution

Related Solutions

Prove that there exist infinitely many positive real numbers r such that the equation 2x +...

If (x,y,z) is a primitive Pythagorean triple, prove that z= 4k+1

Let x, y, z be a primitive Pythagorean triple with y even. Prove that x+y ≡...

Prove that the union of infinitely many countable sets is countable.

How can we use Hilbert's theorem 90 to find all Pythagorean triples?

Prove: There are infinitely many primes of the form 6n − 1 (n is an integer).

Discrete math problem: Prove that there are infinitely many primes of form 4n+3.

Show that if (x,y,z) is a primitive Pythagorean triple, then X and Y cannot both be...

Prove this is true: The sequence {4k + 3} where k ∈ N contains infinitely many...

Prove this is true: The sequence {4k + 3} where k ∈ N contains infinitely many...