YouTube Math Challenge

YouTube Math Challenge
How would you like to be only the second person in the world to discover this rational sequence a^2 + b = c^2
It can be done ,if you don't think so ,tell me .got questions ask . if you leave a comment , one day i will send you the sequence .

If you know anyone who likes math ,please pass it on .I have known this sequence for years and i bet nobody else knows it .

Category:

Education

Tags:

• math
• maths
• mathmatics
• numbers
• arithmatic
• sequence
• challenge
• calculate
• power
• squared
• pythagoras
• natural
• discovery
• unknown
• variables

[PYTHAGORAS101]

nice try , but it is not continuous

it = 0 ,

but the next numbers are 2,3 ,4 ect (in your sequence)

they do not equal 0 according to the fomula a2+b=c2

[Drakeman8]

Ok here it is. There is in fact a real proof of the solution(maybe you already know it). The solution can be found under the assumption this is a geometric series such that (b-x)^2 +b = (b+x)^2. If we expand this we find b=4bx. Then we can divide and find x=1/4.

I realize that this solution requires the assumption that this is a geometric series. But someone trying to find a solution could surely work under different assumptions and ultimately find it in this way. Cheers.

[PYTHAGORAS101]

Thanks 4 your wise comments friend , its very apreciated .Its just a tast of whats to come .This is just a snippit of the big picture .

btw geometry / math are the same thing .

(proof is to come )

[Drakeman8]

Thanks. I know; I was referring to the fact that it's a geometric series (i.e. takes the form of some multiple times x where x is the number in the series). For example, 2, 4, 6, 8 is a geometric series, whereas 1,3,5,7 is not.

[PYTHAGORAS101]

7 is not (geometric ) ,but 1234568 is , they are constructable .(devisions in a circle )

[PassionOfTheChrisT01]

Personally the answer to this isn't really that difficulty. If you were to think about it, since 0^2 + 1 =/= 2^2 and if the later amounts only amount to a higher difference. We have to look forward into the negatives. If B was to be 0, what consecutive numbers when squared would be the same answer.  Therefore the answer to this "math challenge" is simply -1, 0, 1 a=-1, b=0, c=1

[PYTHAGORAS101]

check out YouTube Math challenge 2

[Shortmandesigner]

What about a = -1, b = 0, and c = 1?

[Drakeman8]

Sorry, you're right. The type of series I'm talking about is not a geometric one. The solution still holds, as a result of the fact that the arithmetic difference between consecutive numbers is constant. Therefore we can assume, as is done in my solution, that the former number is some number x less than the middle one, and that the latter number is that same number x more than the middle. That's what I was getting at, I just used incorrect terminology in my explanation.

[Drakeman8]

The reason it must be assumed in my solution is because b is assumed to be the middle number of any three consecutive numbers in the series. Under the assumption it's geometric, the number before would have to be some number x less than the middle and the latter number would have to be that number x greater than the middle. We then plug in the former number, a, as b-x, and the latter number c as b+x and solve for x.