Notice a pattern:

3^2 + 4^2 = 5^2
5^2 + 12^2 = 13^2
7^2 + 24^2 = 25^2
9^2 + 40^2 = 41^2
Conjecture a pattern, test it. Prove it

Question

Notice a pattern:

3^2 + 4^2 = 5^2
5^2 + 12^2 = 13^2
7^2 + 24^2 = 25^2
9^2 + 40^2 = 41^2
Conjecture a pattern, test it. Prove it

anonymous · Answer

3:4:5 is the ratio of a perfect triangle
it holds true for the rest of the numbers too.

anonymous · Answer

its like :
(1+4)^2, then 
(5+8)^2 and then
(13+12)^2 and
(25+16)^2.
can you see the patern now?

anonymous · Answer

this is what i see:

$$(2n + 1)^2 + \left( 4\sum_{i = 1}^{n}i \right)^2 = \left( 1 + 4\sum_{i = 1}^{n}i \right)^2$$

appears to work.

which class is this for btw? might narrow down how we're supposed to solve it.

give feedback plz ^_^