Melody

Find the greatest common factor of all nubmers of the form 2^n*3^(2n) - 1, where n is an integer greater than 1.

\(2^n*3^{2n} - 1=2^n*9^n-1=18^n-1\) 

I think the greatest common factor is probably 1.  

I don't know how to show or prove it though. 

Let the width shown = w     and  the length shown be  h   (for height)

\(\frac{2w}{h}=\frac{h}{w}\\ 2w^2=h^2\\ \sqrt{2}w=h\\ \text{so the ratio of width to length as shown is}\qquad 1:\sqrt2\)

Have you used the distance formula to find the distances yourself yet?

You are welcome :)

I don't answer questions posted by people who are too lazy to remove unwanted dollar signs.

Simple

How many ways can 4 mathematicians sit in a row?  4!

How many ways can 3 physicists sit in a row?  3!

Seat the engineer.

the engineer can have maths people on his left or right, that is 2 ways.

Multiply these three numbers together and you will have your answer.

1.

initial number:5660236326063470

x=58741285

is the result of x*96358742.

how can I compute the x?

You have been given x, there is nothing to compute

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2.and what about numbers where I have only many values = 74*55*55*42*96*1858 , result is 1676962425600

how can I get these numbers when I have only the result, 1858, and number of previous numbers?

No you can't because none of those factors are prime. 

If they were all prime  and you were told how many there were then you could.

Not so politely continued here