I'm the opposite. I don't reckon to be fully awake until 10am, and my brain is positively buzzing at 11pm.

21122012 wrote:

I don't want to answer at once. And that will turn out as in other topic. All will be silent or it is simple to speak: "I don't agree" but won't reason and prove disagreement. I want to arrive now more cunning. That you gradually reached before that I want to tell.

I'm guessing that to do what you want, you have found a formula for prime numbers. :?

Bob

]]>noelevans' method seems to work fine.

Using his method, here are some examples:-

1) 6; 2) 6*2=12; 3&4) 6²+1= 37; 5) 6²-1= 35: **12² + 35² = 37²**

1) 12; 2) 12*2=24; 3&4) 12²+1=145; 5) 12²-1=143: **24²+143²=145²**

1) 17; 2) 17*2=34; 3&4) 17²+1=290; 5) 17²-1=288: **34²+288²=290²**

1) 25; 2) 25*2=50; 3&4) 25²+1=626; 5) 25²-1=624: **50²+624²=626²**

1) 29; 2) 29*2=58; 3&4) 29²+1=842; 5) 29²-1=840: **58²+840²=842²**

The bold-font result is in the order I normally write the equation.

]]>If (x,y,z) is a Pythagorean triple then so is (kx,ky,kz) for integers k>1. And if I recall

correctly all Pythagorean triples can be obtained from these formulas.

Most folks have trouble coming up with more than 2 or 3 Pythagorean triples. I have

taught students to come up with many more by simply:

1) Think of a positive integer >1.

2) Double it. That's the 1st of the triple.

3) Square the number obtained in step 1)

4) Add one to that square. That's the 2nd of the triple.

5) Subtract one from that square. That's the 3rd of the triple.

Of course that's just the triple above with b set equal to 1 and a>1.

]]>I have moved it.

]]>Do you already have an answer to the problem?

I don't want to answer at once. And that will turn out as in other topic. All will be silent or it is simple to speak: "I don't agree" but won't reason and prove disagreement. I want to arrive now more cunning. That you gradually reached before that I want to tell.

Then you won't be able to tell that you aren't right!

]]>I remember seeing a proof that all Pythagorean triplets are of the form

a-b, 2*sqrt(a*b), a+b

for natural a and b.

No!

Yes?

You look here. Here important intermediate question: As the formula

mean if an indicator

of a general view will look: n? !

a-b, 2*sqrt(a*b), a+b

for natural a and b.

]]>- is ONE;

- is TWO;

- is THREE;

...

You understand?

HOW MANY?

]]>