The proof Fermat hinted to was about the difference between squares. All whole numbers taken to a power greater than two (n^3) can be represented as the difference between two whole squares (x^2 - y^2). These differences can then be shown as the sum of consecutive odd numbers:
When you examine the odd number series that results from each base, you'll discover that there will always be a gap if you try and combine two odd number series together, which explains Fermat's little joke about margins. The same trick works for higher powers.
It's not that hard people. Stop believing everything you're told about how "hard" something is.
HINT:
The number of odd numbers in the series exactly matches the starting square base number
I'm working to understand this, but I can't seem to fit it together. Following Feynman's lead in this sort of thing, can you give me an explicit example of why the equation x^13+y^13=z^13 has no solutions? Or even just use your technique to explain why x^5+y^5=z^5 has no solutions?
It looks like you edited this comment, but I'm serious. I'm trying to understand your proof, but I'm having trouble seeing what the steps are for higher powers than 3 or 4. I already know the proofs for then cases n=3 and n=4, but I can't see how what you say works in the case, say, n=5, or n=13.
Seriously, can you walk us through the steps of why x^5+y^5=z^5 has no (non-trivial) solutions?
And to be fair, there are cases where, say, undergrads have proven significant results that had been outstanding for a long time. Proving that prime recognition is in P is one such case. but in that case they published a complete, clear paper. In this case I can't really see what you're saying you've done, or why it's true, which is why a walk-through of the case n=5 would be so helpful.
Thanks.
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For anyone interested, this is what the comment used to say ...
The series of odd numbers must be consecutive and they simply are not when you add two different series together for all powers greater than two. It's okay. You'll get it.
1) a whole number, n, taken
to a power greater than two
2) can be represented as a
consecutive series of odd
numbers
3) where there will always be
a gap in the series between
consecutive base numbers,
for all p and p+1
4) therefore there will be
a gap for all p and p+n,
n>=1 combinations
Consecutive base numbers will necessarily alternate between even and odd. So even the closest base numbers still have a gap between their resulting odd number series, which only increases as the distance between base numbers increases.
'ox_n appears to be trying to prove (by a pigeonhole agument) that the equation x^n + y^n = z^n in unsolvable for _some z_. That's much weaker than proving that it is unsatisfiable at _every_ z.
> It's not that hard people. Stop believing everything you're told about how "hard" something is.
There are still many problems in physics and mathematics which are considered "hard" (e.g., dark energy, Riemann hypothesis, etc). Can we crack them by simply adopting your positive mindset?
I don't think the "you can do anything" mindset works in real life. It helps self-help book authors sell their stuff, but it's not a good strategy to live by. (Incidentally, this reminds me of Key & Peele's "You can fly" sketch).
What does work though is this: advanced formal education in a topic. Once you have that you can start thinking on how to solve some simple open problems. And if you are lucky and turn out to be extremely smart, you may be able to tackle more challenging problems. Some amount of self confidence may also you to keep going but doesn't make you a genius overnight.
Simply going to a mindset where things are 'not hard' is closer to delusion than it is to anything else.
In academia we get often emails from people who solved quantum gravity (e.g. using fire), show us how einstein is wrong (e.g. using a pendelum), etc. I'm pretty sure they also convinced themselves to "Stop believing everything they're told about how "hard" something is"
Oh man, that reminds me of an experience I had in college. I was working with the aerospace department on their fusion reactor (I was just writing software to help them process data from it, not involved in the science itself). My boss kept getting calls from crackpots who'd go on and on and on about their bogus theories, and how they were being shut out of the mainstream by small minded fools, etc etc.
It was pretty frustrating. He was too nice a guy to tell them off or even cut them off quickly.
My advice to any crackpots who are really sure they're actually geniuses: Get into the stock market (with a SMALL investment). If you're as smart as you think you are, you can find an angle and turn $100 into $1,000,000 or more, and then if anything it'll be GOOD that nobody ever believed in you. I've run across arbitrage opportunities that would have made me fiendishly rich if I'd noticed them sooner myself, believe it or not. Just be careful and don't mess with box spreads.
No, but even those from "left field", if genuine, tend to take the time and care to write things up properly, to use the nomenclature of the field, to address obvious potential concerns up front.
If you're asserting something that's likely to encounter resistance, it's worth being clear and careful.
Pulsar data itself is likely not under copyright, but a graph of it can be under copyright protection if enough creative effort is involved. However that graph contains very little creative decision, so it would be a hard case to win if the publisher claimed ownership.
Does it cross the threshold of originality? It is just 3d line chart. Any it hardly matters what data is actually plotted, so I assume they used something random.
The proof Fermat hinted to was about the difference between squares. All whole numbers taken to a power greater than two (n^3) can be represented as the difference between two whole squares (x^2 - y^2). These differences can then be shown as the sum of consecutive odd numbers:
When you examine the odd number series that results from each base, you'll discover that there will always be a gap if you try and combine two odd number series together, which explains Fermat's little joke about margins. The same trick works for higher powers.It's not that hard people. Stop believing everything you're told about how "hard" something is.
HINT: The number of odd numbers in the series exactly matches the starting square base number