Re: 7-adic distance in Q7

So, you are looking for such that . So, suppose (it can be 2 or 5). Then , so . That gives , and a carry of 1. So, . This gives as you suggested. Again, the carry is 1. Then, , so and the carry is 3. Next, . So, , and the carry is 5. So, I don't know how you calculated the square root of 305, but I got a very different result.

Re: 7-adic distance in Q7

yes ur right, i got some mistakes of my caculation. now, i got the new representation for root 305 should be right: 2.22345... or

5.4432....

and my question is how to caculate the distance between -1/3

and root of 305 in Q7 (i.e. w.r.t the norm|.|p) Hints for the question is:

compute first few terms of 7-adic expansion of -1/3 and root 305 .

Now , i dont know how to consider the distance..

Re: 7-adic distance in Q7

The easiest way to check if a solution is correct is to use evaluate its geometric sum: . So, you found the correct representation for . So, is the minimum distance between the possible square roots of . So, if and , and both of them squared give , the 7-adic distance is

Re: 7-adic distance in Q7

sorry, do you mean if i continue to do the method for more digits of 2.22345... or 5.4432.... then i can get k and -k as ur post?? but how could u ensure that for 2.22345... , u can only get 5 on the digits after 4？？？

Re: 7-adic distance in Q7

You are writing . That is not a notation I am familiar with. I am used to which means . I suspect they mean the same thing. I am using only digits to the left of the decimal place. You are using digits to the right of the decimal place. I learned that . Anyway, using your notation, you want . Note that .

Re: 7-adic distance in Q7

Thats clear for me now. thanks a lot

Re: 7-adic distance in Q7

How did you calculate the 7-adic expansion of square root 305? i honestly cannot do it

Re: 7-adic distance in Q7

Quote:

Originally Posted by

**lahuxixi** How did you calculate the 7-adic expansion of square root 305? i honestly cannot do it

me too

Re: 7-adic distance in Q7

Calculate it digit-by-digit. I went through it in post #2.

Re: 7-adic distance in Q7

I don't need the answer to the question of this thread. I want to ask you about the method of calculating the expansion for other cases. Thank you

Re: 7-adic distance in Q7

Quote:

Originally Posted by

**SlipEternal**

what does this mean?