Math Is Fun Forum

How to write ">" in LaTeX?

For lineal d.e. we can use the this

Not.
(x-1)(x^2-2x-15)=x^3-2x^2-15x-x^2+2x+15=x^3-3x^2-13x+15

Let look at the neightbours of n in chain with length n amd maxNumber n:
{...,x,n,y,...}
We take that n>x>y. Then n+x and n+y are perfect squares, so:

n+x > n+y =>

Let

Then

so

So when

there does not exist chain with Length n and MaxNumber n.
From the upper equation we get:

=>

=>
for 0 ≤ n < 5.8 there doesn't exist that kind of chain, so

n>5.

John, i' explain later.

When you have the proof please don't post it immediately. I want to test myself.

Let start.
for any square s
s==0,1(mod 4).

So the sum of two conseuense numbers must be ==0,1(mod 4).
We have this cases:
If n == 0 (mod 4) then the neightbours of n must be == 0,1 (mod 4)
If n == 1 (mod 4) then the neightbours of n must be == 3,0 (mod 4)
If n == 2 (mod 4) then the neightbours of n must be == 2,3 (mod 4)
If n == 3 (mod 4) then the neightbours of n must be == 1,2 (mod 4)

That's a begining.

Yes, but actually length =0 and length=1 are trivial.

I thing for computing these we might use come algoritm simular to the labyrinth algoritm.

!!!!