Φ¹² 60stars Astrology Season Essay Φ¹² ” The very edge of the rule "

60stars  Astrology Season  Essay

English  version

By TOKYO-TANUKI

Φ¹²　60stars  Astrology Season  Essay　Φ¹²　” The very edge of the rule " 

１．About Fermat numbers — as I have written before —  
when "n" is an integer, the equation  

【2^(2ⁿ⁻¹ − 1)】X² − X − 【2^(2ⁿ⁻¹ − 1)】 = 0  

has the solution,  

X= 

{ 1 ± √( 1 + 2² × 【2^(2ⁿ⁻¹ − 1)】² ) } / { 2 × 【2^(2ⁿ⁻¹ − 1)】 }  

......Now, if we call the part inside the square root,  
1 + 2² × 【2^(2ⁿ⁻¹ − 1)】², “F(n),” 

Then:  

when n = 1,  
F(1) = 1 + 2² × 1² = 5  

when n = 2,  
F(2) = 1 + 2² × (2¹)² = 17  

when n = 3,  
F(3) = 1 + 2² × (2³)² = 257  

when n = 4,  
F(4) = 1 + 2² × (2⁷)² = 65,537  

In this way, the Fermat numbers appear.  

......I already wrote this before, maybe on "X" .  

2.  In other words, the "Fermat numbers" are still within  
the framework of the ordinary quadratic formula.  

So even if we call them revolutionary,  
they are not creating a completely new rule.  

....In contrast, in the case of " X + 1 = X ",  

no matter how many times we square or cube both sides,  
we cannot find an answer by using the quadratic formula.  

In this case, "X" is outside the rules.  
This is what we call an “error.”  

....Now, why is Tanuki talking about this?  

Because, depending on how we look at it,  
the Fermat numbers represent the very edge of the rule itself.  

3. .......Ah —of course, what comes next is just the words of an amateur,  so don’t mind too much. Tanu-chan is from the humanities, after all.  

At present, there is something called the "a b c  conjecture" .  

For a triple of natural numbers a, b, c (where c = a + b)  
that are mutually coprime,  let d = rad (abc). 

Then probably  
c < d^(1 + ε),  

and perhaps  
c < d².  

That’s what it says.  

Here, a mathematics professor at a Japanese university  
says he is reexamining the entangled relationship between multiplication and addition.  

But, well, everyone is confused,  and it has caused quite a commotion.  

It’s almost like a quarrel.  

.....Whether that story is right or wrong,  Tanuki has no idea—  
but the theme is a little similar to Fermat numbers. 

Fermat numbers, in the form of powers of powers,  
raise the issue of the relationship between addition and multiplication, and also anticipate a relationship with prime numbers.  

So, even if they ultimately turn out to be wrong,  
I think the root of interest is probably the same.  

.................That’s just Tanuki’s instinct as an animal!  

Probably, it means “Let’s look once again  
at the relationship between primes, powers, addition, and multiplication!”  

In other words, multiplication  
may look like a simplification of addition—  but perhaps it’s not exactly so??  

By trying to solve what is believed to be an absolute problem (or rule),  prime numbers also become involved—  that’s what I think.  

Of course, everything above is merely Tanu-chan’s impression , or rather, delusion as a small animal—  an animal’s way of thinking.

（....to be continued)



Tanu-chan💓　TOKYO-TANUKKO💛