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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 217

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

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

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9090916761247679844122304328506045308491

*Last edited by Stangerzv (2013-12-10 18:43:41)*

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The result is not true for *p*=11. However, if *p* is odd and not divisible by 11, then it will be true. Here is the proof.

Since *p* is odd, we have

since 10 ≡ −1 (mod 11). Also

by Fermats little theorem. (This only works if *p* is not divisible by 11.) Hence

*Last edited by Nehushtan (2013-12-10 23:47:58)*

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**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 217

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

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