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Hi cmowla

This is part of new way to find an alternative proof for Fermat's Last Theorem, I have stumbled at this part for power n=3.

n=0 is not a trivial because when n=0,

So far I managed to get through up to this stage:

For divisibility by 3, let n=3x-2, then

Therefore,

Trivial solution is x=1 and alpha=1

There should be no other whole number solution other than the trivial solution.

Another problem is to find the proof that the only whole number solution for alpha is 1 when n=1 for the following equation:

Otherwise please find the counter-examples.

Hi bobbym

Okay, I have edited it. This is what happened if you play around with the infinity. I am always skeptic with it, but seeing Ramanujan and Euler played with it and made remarkable things. Maybe I can also using it

too.

Hi bobbym, thanks for the even one. I am not sure my method is ok or not, lets say,

for odd n

then

Since n=odd,

can never be a perfect square.hi bobbym

I know there exist the proof for n=3 but I am working for a simple and short proof and this proof is not the same like the way the proof for n=3 done by Euler etc. I have reduced the fermat's last theorem into polynomials using my sums of power formulation and I am trying to work it out for smaller power and later on the generalize proof for all n.

I think the equation could be factorized as follows:

For even n:

and other than alpha=0 or 1, the equation below holds.

Just need to find the proof.

Hi bobbym, I am looking for other than the trivial solutions.

**Stangerzv**- Replies: 24

Can anyone help me to find the proof that the only whole number solution for alpha as in the equation below is 1. Otherwise please find any other solutions (counter-examples)

Hi bobym

For

n=26 gives the highest prime for for n ≤ 4000.

Hi bobbym

I haven't tried it yet but for

n=26 gives the highest prime for n≤ 8000

Hi bobbym

I have done with the calculation for

n=26 is the highest prime for n ≤ 5000.

There are only three double primes by combining the equations above. The double prime generalize equation is gives as follows:

n=6, Ps=701, 739

n=10, Ps=3628747, 3628853

n=26, Ps=403291461126605635583999651, 403291461126605635584000349

Another version of the prime yields 6 primes so far

n=2, Ps=-1+2+1*2=3

n=6, Ps=-1+2+3+4+5+6+1*2*3*4*5*6=739

n=10, Ps=-1+2+3+4+5+6+7+8+9+10+1*2*3*4*5*6*7*8*9*10=3628853

n=14, Ps=-1+2+3+4+5+6+7+8+9+10+11+12+13+14+1*2*3*4*5*6*7*8*9*10*11*12*13*14=87178291303

n=22, Ps=-1+2+3+4+5+6+7+8+9+10+11+12+13+14+..+22+1*2*3*4*5*6*7*8*9*10*11*12*13*14*..*22=1124000727777607680251

n=26, Ps=-1+2+3+4+5+6+7+8+9+10+11+12+13+14+..+26+1*2*3*4*5*6*7*8*9*10*11*12*13*14*..*26=403291461126605635584000349

Hi bobbym

Sorry there is a mistake with the minus sign, I've edited it. Basically 1-2-3-..n=2-(1+2+3) and 1*2*..n=n!, the first equation is the generalize equation for the primes.

**Stangerzv**- Replies: 10

The equation is given as follows:

Example:

n=1, Ps=1+1=2

n=3, Ps=1-2-3+1*2*3=2

n=5, Ps=1-2-3-4-5+1*2*3*4*5=107

n=6, Ps=1-2-3-4-5-6+1*2*3*4*5*6=701

n=10, Ps=1-2-3-4-5-6-7-8-9-10+1*2*3*4*5*6*7*8*9*10=3628747

n=13, Ps=1-2-3-4-5-6-7-8-9-10-11-12-13+1*2*3*4*5*6*7*8*9*10*11*12*13=6227020711

n=26, Ps=1-2-3-4-5-6-7-8-9-10-11-12-13-..-26+1*2*3*4*5*6*7*8*9*10*11*12*13*..26=403291461126605635583999651

Thanks Nehustan, I didn't notice when p=11, the same applies to p=3 for mod(3).

**Stangerzv**- Replies: 2

I have encountered a new property in which I hope nobody has found it yet.

The equation is given as follows:

If p is prime and greater than 3 then,

In other words,

If p is prime then

is a whole number.Prime generated y is given as follows:

y(59)=9090909090909090909090909090909090909090955556068481876491

y(3109)=9090909090909090909090909090 9090909090909090909090909090909090909090

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9090916761247679844122304328506045308491

**Stangerzv**- Replies: 2

I have encountered a new property in which I hope nobody has found it yet.

The equation is given as follows:

If p is prime and greater than 3 then,

In other words,

If p is prime then

is a whole number.Prime generated y is given as follows:

y(7)=- 90825083

y(47)=33333333333333333333333333333315800289254723317

y(79)=3 333333333333333333333333333333333333333333333333333333333330177241305791050933

y(83)=33333333333333333333333333333333333333333333333333333333333333328161319604264715517

Hi Bobbym

It would take some times and I would let you know when it is done.