P-adic Valuation
Let p be a prime, for example, p=2. Then if you want to find the
2-adic valuation of 1872, you would write
1872 = 2 4
*177
so the 2-adic valuation of 1872 is 4. We write
ν2(1872)=4
More formally, if you want to find the p-adic valuation of n, you
write
n = p m*a
where p does not divide a
and the p-adic valuation of n is m. We write
νp(n)=m