1. Nov 19, 2013

### Funky1981

1. The problem statement, all variables and given/known data
Find the 7-adic distance between -1/3 and the square root of 305 in Q7

2. The attempt at a solution
My solution is write the 7-adic expansion of -1/3 and square root of 305

the 7-adic expansion of -1/3 := 2 +2*7+2*(7^2)+.... =2.2222222(index 7)

the 7-adic expansion of square root of 305:= 2.22345....(index7) or 5.4432.... this is one representation of root of 305 but there is another representation of 7-adic expansion

Hence they have the same 7-adic expansion . therefore the distance is 0 in Q7?

Is my attemption right? ( i am not sure whether i caculated these two 7-adic expansion in a right way)

Last edited: Nov 19, 2013