Is there an easier prime factorization method for the sum of a prime's powers?

Mathematics Asked by Ifn47 on August 3, 2020

I need to obtain prime factorizations of numbers of the type: $sum_{i=0}^n p^i$, for any prime number $p$ (not the same one each time).

Do you know if there is a quicker algorithm to calculate these factorizations than those used for other natural numbers?

I don’t know if there is a known solution. My only lead is that all Mersenne primes are of the form $sum_{i=0}^n 2^i$.

Edit: by prime factorization I mean, for example, if $p$ is 3 and $n$ is 6, the number is 364, and the prime factorization I’m looking for is 2^2, 7 and 13.

prime factorization prime numbers

One Answer

You have a geometric series, so $sum_{i=0}^n p^i=frac {p^{n+1}-1}{p-1}$. When the prime is $2$ this does not give a factorization because the denominator is $1$. For all other primes it does.

Correct answer by Ross Millikan on August 3, 2020

Is there an easier prime factorization method for the sum of a prime's powers?

One Answer

Add your own answers!

Related Questions

What is the solution of this summation?

Number of fixed points of a random permutation

Find $a$, $b$ such that $x^2 – x -1$ is a factor of $ax^9 + bx^8 + 1$

“Standard theorem on differential equations” that implies a function is analytic

Identity up to isomorphism treated as identity in proof

Burnside’s Lemma bracelet with beads in 2 colours (uneven cardinality)

Prove $2^{lceil lg (n-1) rceil} ge n-1$

Identify boolean function that satisfies some constrains

How to show that the curve $ay^2=x(x-a)(x-b)$ has two and only two points of inflexion?

volume under a 3-d curve

Groups of $3$ out of $23$ s.t. all students cooperate exactly once

(Manifolds) Prove the following is a sufficient condition for a function to be a morphism between manifolds

existence of countably additive measure for Borel subsets of $[0,1]$

Are the two spans equal?

Simplifying iterated sums where the upper bound is the next index

Mathematical Writing: Can objects in a definition be assigned any name, even though this name is used elsewhere in the text?

$T:P_nlongrightarrow P_n : Tp(t)=frac{d}{dt}p(t)text{ Find the norm of the operator}$

Method to solve an equation

Prove that $sum_{n=1}^infty frac{x^{2n}}{(n+x)^2}$ converges uniformly on $S=[0,1]$

Find moment generating function for $sqrt{n}(overline{X}-1)$

Ask a Question