Question
Asked Feb 4, 2019
73 views

Let a, b, and c be integers such that a^2+b^2=c^2. Prove at least one of a and b is even.

check_circle

Expert Answer

Step 1

It has been given to us that a, b, c are integers and a2 + b2 = c2.                                                     And we need to prove that for the above equation to be true at least one of a, b is to be even.                                                                                                                                                                                       We can prove this by contradiction as below: -                                                                                           Let us consider that both of a and b are odd integer.

Then we can write a = 2k + 1 and b = 2p + 1 for integers k and p.

Therefore, we will have the calculation as below: -

fullscreen
Step 2

Now we will consider two different cases:

Case I: If c is even: then c is divisible by 2 and so c2 is divisible by 4.

However, a2 +...

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.

Related Advanced Math Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: Comlex Analysis, only need part d.

A: The function is

question_answer

Q: I’m working on #25

A: To multiply by a suitable integtating factor and thereby find the solution of the given differential...

question_answer

Q: z is a complex variable z=x+iy pic attached with question  Evaluate using L’Hospital’s rule

A: To calculate the limit of the given indeterminate form using L'Hosptial rule

question_answer

Q: Prove or disprove: Let a and b be integers and let p be a prime number. if p | ab then p | a or p | ...

A: The above statement is termed as Euclid’s Lemma.We will prove it in two ways: -First one: -Let us co...

question_answer

Q: For an initial investment of 100, an investment yields returns of Xi  at the end of period i for i=1...

A: Given that, the initial investment is 100 and the investment yield is X1 and X2 at the end of period...

question_answer

Q: 5.2.6.B       Discrete Mathematics This is a dublicate please answer the question as quickly as poss...

A: Known fact:Base step: Show it is true for first case, usually n =1.Induction step: Show that if n = ...

question_answer

Q: I need the solution of Question no 6 only

A: Let the constant perimeter be P = a+b+c, where a, b, c are the sides of the triangle. The triangle a...

question_answer

Q: Suppose f(z) is analytic for |z| <= 1, and |f(z)| >=1. If f(0) =1, prove that f(z) is constant...

A: To prove that the given conditions on the analytic function force it to be the constant function f(z...

question_answer

Q: Differential equations. Find the particular solutions to the given systems of equations. Please refe...

A: (a) The differential equation is given as