All Questions
Tagged with prime-factorization factorial
8
questions
4
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Proof that each prime power of ${2n \choose n}$ is $\leq \log_p 2n$
I'm trying to work through this proof of the prime number theorem.
Def: Let $P_p(x)$ be the prime power of $p$ in the prime factorization of $x$. I.e. for any natural number $x$, $x = \prod_{p\in \...
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2
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Total number of divisors of factorial of a number
I came across a problem of how to calculate total number of divisors of factorial of a number. I know that total number of divisor of a number $n= p_1^a p_2^b p_3^c $ is $(a+1)*(b+1)*(c+1)$ where $a,...
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Factorials and Prime Factors
I need to write a program to input a number and output it's factorial in the form:
$4!=(2^3)(3^1)$
$5!=(2^3)(3^1)(5^1)$
I'm now having trouble trying to figure out how could I take a number and get ...
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(1) Sum of two factorials in two ways; (2) Value of $a^{2010}+a^{2010}+1$ given $a^4+a^3+a^2+a+1=0$.
Question $1$:
Does there exist an integer $z$ that can be written in two different ways as $z=x!+y!$,where $x,y\in \mathbb N$ and $x\leq y$?
Answer: $0!=1!$ so $0!+2!=3=1!+2!$
Question $2$:
If $...
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Can we conclude $n=p-1$?
Let $\ n\ $ be a positive integer and $\ p\ $ a prime number such that $$\ p^2\mid (2n)! + n! + 1$$ The only pairs $\ (n,p)\ $ I found so far are
$(1,2)$ , $(2,3)$ , $(10,11)$ , $(106,107)$ , $(4930,...
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Find the prime factor decomposition of $100!$ and determine how many zeros terminates the representation of that number. [duplicate]
Find the prime factor decomposition of $100!$ and determine how many zeros terminates the representation of that number.
Actually, I know a way to solve this, but even if it is very large and ...
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2
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Integer factorization: What is the meaning of $d^2 - kc = e^2$
I found an interesting behavior when placing the integer factorization problem in to geometry, I call it pyramid factoring.
Lets assume we have $c$ boxes and we want to order them in to rectangle. ...
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Express $11!$ and $\binom{23}{11}$ as products of their prime factors
I'm a bit stuck on how to figure this question out without a calculator and what kind of working I'm supposed to show. Any help would be appreciated, thank you. $\ddot\smile$
Factorise $11!$ and $\...
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