Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 240

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

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090909090909090909090909090909090909090

9090916761247679844122304328506045308491

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

Offline

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)*

Offline

**Stangerzv****Member**- Registered: 2012-01-30
- Posts: 240

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

Offline