What is P in number theory?

In mathematics, the p-adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.

What are p-adic numbers used for?

The p-adic absolute value gives us a new way to measure the distance between two numbers. The p-adic distance between two numbers x and y is the p-adic absolute value of the number x-y.

Is the P-ADIC integers complete?

The p-adic integers can also be seen as the completion of the integers with respect to a p-adic metric. Let us introduce a p-adic valuation on the integers, which we will extend to Zp.

What is the p-adic metric?

A -adic number is an extension of the field of rationals such that congruences modulo powers of a fixed prime are related to proximity in the so called ” -adic metric.”

What does P stand for in calculus?

Usage. The capital Latin letter P is used in math as a variable. For example, the symbol is often used to represent a point in the cartesian coordinate system. The symbol is also used in statistics to represent a probability distribution.

What is P equation?

The perimeter of a square field is given by the equation P = 2l + 2w, where P represents the perimeter, l represents the length of the field, and w represents the width of the field.

Who invented P-ADIC numbers?

mathematician Kurt Hensel
The p-adic numbers were invented at the beginning of the twentieth century by the German mathematician Kurt Hensel (1861–1941). The aim was to make the methods of power series expansions, which play such a dominant role in the theory of functions, available to the theory of numbers as well.

How do you calculate P-ADIC expansion?

The proof of Theorem 3.1 gives an algorithm to compute the p-adic expansion of any rational number in Zp: (1) Assume r < 0. (If r > 0, apply the rest of the algorithm to −r and then negate with (2.2) to get the expansion for r.) (2) If r ∈ Z<0 then write r = −R and pick j ≥ 1 such that R < pj.

How do you find p-value statistics?

If your test statistic is positive, first find the probability that Z is greater than your test statistic (look up your test statistic on the Z-table, find its corresponding probability, and subtract it from one). Then double this result to get the p-value.