Friday

March 6, 2015

March 6, 2015

Posted by **Kevin** on Wednesday, February 22, 2012 at 6:24am.

- Math -
**MathMate**, Wednesday, February 22, 2012 at 7:43amVerification:

5²=25=12+13

5²+12²=25+144=169=13²

Therefore it works.

Proof:

Let the odd number be a=2k+1,

where k=any integer.

(2k+1)²=4k²+4k+1

The two consecutive numbers are therefore

b=2k²+2k and c=2k²+2k+1

Now calculate the pythagorean sum of a and b:

a²+b²

=(2k+1)²+(2k²+2k)²

=4k^4+8k^3+8k²+4k+1

=(2k²+2k+1)²

=c²

**Answer this Question**

**Related Questions**

Math - How to Generate Pythagorean Triples using an Odd Number 1. Start with an ...

Maths - The first odd number can be expressed as 1 = 1squared - 0squared. The ...

Math - 5 times the least of three consecutive odd numbers is 35 more than twice ...

Algebra - 5 times the least of three consecutive odd numbers is 35 more than ...

Math - Most natural numbers can be expressed as a sum of two or ore consecutive ...

math check - Posted by TchrWill on Thursday, July 14, 2005 at 5:44pm. 2.)The sum...

math algebra - Find 3 consecutive odd numbers where the product of the smaller ...

SUMS? - what is the sum of the first towo odd numbers? what s the sum of the ...

maths - Fill in the blanks- 1). the sum of two consecutive odd numbers is 84, ...

Math - Find the sum of the first 35 consecutive odd numbers. What is the sum of ...