<Dd> ⇒ − 1 7 =...142857142857142857 (\ displaystyle \ Rightarrow - (\ dfrac (1) (7)) = \ dots 142857142857142857) </Dd> <Dd> ⇒ − 6 7 =...142857142857142857 × 6 =...857142857142857142 (\ displaystyle \ Rightarrow - (\ dfrac (6) (7)) = \ dots 142857142857142857 \ times 6 = \ dots 857142857142857142) </Dd> <Dd> ⇒ 1 7 = − 6 7 + 1 =...857142857142857143 . (\ displaystyle \ Rightarrow (\ dfrac (1) (7)) = - (\ dfrac (6) (7)) + 1 = \ dots 857142857142857143 .) </Dd> <P> Generalizing the last example, we can find a 10 - adic expansion with no digits to the right of the decimal point for any rational number p / q such that q is co-prime to 10; Euler's theorem guarantees that if q is co-prime to 10, then there is an n such that 10 − 1 is a multiple of q . The other rational numbers can be expressed as 10 - adic numbers with some digits after the decimal point . </P>

What is the smallest positive representative of the residue class of 83 in latex mathbb z_ 15 z 15