p-adic absolute value

Any nonzero rational number x can be represented by x = (p^a r)/s, where p is a prime number, r and s are integers not divisible by p, and a is a unique integer. The p-adic norm of x is then defined by left bracketing bar x right bracketing bar _p = p^(-a). Also define the p-adic value left bracketing bar 0 right bracketing bar _p = 0. As an example, consider the fraction 140/297 = 2^2·3^(-3)·5·7·11^(-1).

greatest dividing exponent | p-adic number