24185

In Generating Triples I am going to answer Alison's part of the question. It says that hypotenuse (answer) is two units longer than one of the other sides.The question is;
Can you find a formula for generating Pythagorean Triples like Alison's?
Can you prove that your formula works?
I will continue this on a word document.
So the three examples they give are;
4²+3²=5²
6²+8²=10²
8²+15²=17²
There is a pattern here (from left to right) the first number goes up by 2. The second number goes up by 5 then by 7 so it only makes sense that in the next equation the second number would be (15+9)=24. The third number again goes up by 5 then 7 so the third number should be
(17+9) =26
Using this info I can make the accurate assumption that the next equation in line will be;
10²+24²=26². Now to prove this, 10²=100 and 24²=576 so 100+576=676. 26²=676. Hopefully this will be enough proof that this formula is correct.
The next two equations in line will be;
12²+35²=37²
14²+48²=50²
Hopefully you think this is correct and you can post this on the main page.