All Questions
22
questions
26
votes
1
answer
536
views
Prime factor wanted of the huge number $\sum_{j=1}^{10} j!^{j!}$
What is the smallest prime factor of $$\sum_{j=1}^{10} j!^{j!}$$ ?
Trial :
This number has $23\ 804\ 069$ digits , so if it were prime it would be a record prime. I do not think however that this ...
- 85.1k
4
votes
0
answers
84
views
Finite many primes for every positive integer $b$?
Consider the function $$f(a,b):=\sum_{j=0}^a (bj)!=1+b!+(2b)!+\cdots +(ab)!$$
Given a positive integer $b$ , are there always only a finite number of positive integers $a$ such that $f(a,b)$ is prime ...
- 85.1k
0
votes
1
answer
343
views
Another Doubt Regarding Brocard's Problem, Specifically about Where I Can Proceed after Prime Factorisation
I know this can draw downvotes as it's not a complete solution or sounds more like an opinion poll (or perhaps this must have appeared elsewhere, in which case you're free to let me know), but I would ...
- 1,573
2
votes
1
answer
85
views
Factorials and Place Value
I recently came across this question from a non-calculator exercise. The units and tens place value digits I can see as $0$ and $0$ since in $12!$ we have $10*5*2=100$ but is there a way to find $a$ ...
- 91
2
votes
1
answer
2k
views
Find the power of a prime in the prime factorization of a large factorial
I have been trying to work through the following exercise:
Find the power of $5$ in the prime factorization of $2020!$.
So far I have worked out that the prime factorization of $2020$ is $2^2 \cdot 5^...
- 143
6
votes
0
answers
100
views
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,...
- 85.1k
0
votes
1
answer
67
views
Is the sequence infinite? Finite? Is there a general formula to determine n th term?
Sequence of numbers whose factorial on prime factorisation contains prime powers of prime numbers, whose power is greater than $1$ or contains multiplicity of one for all prime numbers less than equal ...
1
vote
2
answers
86
views
To determine multiplicity of $2$ in $n!$ [duplicate]
Is there a general formula for determining multiplicity of $2$ in $n!\;?$
I was working on a Sequence containing subsequences of 0,1. 0 is meant for even quotient, 1 for odd quotient.
Start with k=3,...
58
votes
2
answers
8k
views
Can I search for factors of $\ (11!)!+11!+1\ $ efficiently?
Is the number $$(11!)!+11!+1$$ a prime number ?
I do not expect that a probable-prime-test is feasible, but if someone actually wants to let it run, this would of course be very nice. The main hope ...
- 85.1k
1
vote
0
answers
45
views
Number dividing the factorial of a lowest prime
I would like to ask a probably simple question but I am not sure how to make it rigorous.
Let $p$ be a prime and $n$ a natural number whose lowest prime factor is $p$. If a natural number $x$ divides ...
- 727
1
vote
3
answers
356
views
Power of prime in prime factorization of a factorial.
Please advise on how to arrive at solution for determining the power of 17 in the prime factorization of 2890!
Also, is there a short-cut?
So far I know:
Prime factorization of 2890 = 2 x 5 x 17^2
...
- 131
0
votes
1
answer
64
views
How to count Terminal Zeros from subtraction
How do you count the number of zeros that the subtraction 100$^{100}$ - 100! ends in? In particular, I want to know exactly why my approach is wrong, because I know from my source that the answer is ...
1
vote
2
answers
483
views
Prime factorization of factorials
Is there a way given a sequence of naturals $a_1, a_2, ..., a_k$ to determine whether $c=n!$ for some number $n$ where
$$ c = 2^{a_1} 3^{a_2}5^{a_3}7^{a_4}...$$ (2,3,5,7,... - primes)
- 593
-2
votes
0
answers
43
views
Divisor Problem [closed]
Express the numbers $11! = 39,916,800$ and the binomial coefficient $\binom {23} {11}$, each as products of their prime factors. Do this without using your calculator in any way. Use this to calculate ...
0
votes
2
answers
362
views
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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