All Questions
Tagged with prime-factorization factorial
5
questions with no upvoted or accepted answers
6
votes
0
answers
100
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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,...
- 85.1k
4
votes
0
answers
84
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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
4
votes
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119
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If $x$ and $y$ are positive integers then $\frac{(2x)!(2y)!}{x!y!(x+y)!}$ is an integer
If $x$ and $y$ are positive integers then $\frac{(2x)!(2y)!}{x!y!(x+y)!}$ is an integer
I have to show that the proposition above is true for any $x,y\in\mathbb{Z^+}$ by means of Legendre's formula.....
- 3,457
1
vote
0
answers
62
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Numbers $n$ such that $n!$ has all of its exponents odd
(First paragraph for motivation, second paragraph the actual problem)
I usually have to be on a stand as an embassador for my major (math) for highschoolers, and we usually have problems written on a ...
- 899
1
vote
0
answers
45
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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 ...
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