All Questions
46
questions
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146
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How do we get the number of prime divisors?
We have a natural square-free number $n$ such that $2^5\cdot 3^6\cdot 5^4\equiv 0 \pmod {\tau(n)}$.
Which is the maximum number of different primes that can divide $n$ ?
$$$$
We have that $\tau(n)$ is ...
- 14k
3
votes
0
answers
92
views
Are there infinite many primes $\ p\ $ that cannot divide $\ 3^n+5^n+7^n\ $?
Let $\ M\ $ be the set of the prime numbers $\ p\ $ such that $\ p\nmid 3^n+5^n+7^n\ $ for every positive integer $\ n\ $ , in short the set of the prime numbers that cannot divide $\ 3^n+5^n+7^n\ $.
...
- 85.1k
-1
votes
2
answers
124
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How to understand special prime factorization method
Normally when we want to find the Prime Factorization of a number, we will keep dividing that number by the smallest prime number (2), until it can't be divided then we move on to the next prime ...
1
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0
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116
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How many positive divisors of 7560 are coprime to 15?
I'm trying to find the amount of positive divisors of $7560$ that are coprime to $15$.
I do know how to find the total number of positive divisors a number has but I am not sure how finding those who ...
- 11
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0
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30
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Why for every range of N numbers, there are always approximately 0.392*N numbers which contains perfect squares as factors? [duplicate]
As to my current understanding, when simplifying radicands of roots what we are really doing is checking if this said number contains a perfect square number as a factor. Studying the distribution of ...
-1
votes
2
answers
499
views
Let $n$ be a positive integer relatively prime with $10$. Prove that the digits of hundreds of $n^{20}$ is even. [closed]
Let $n$ be a positive integer relatively prime with $10$. Prove that the hundreds digit of $n^{20}$ is even.
I know this has something to do with $\bmod 1000$, I'm just not sure how to write a proof ...
-1
votes
2
answers
50
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Prove that $a|p+1$ if and only if ${\frac{a}{p} = \frac{1}{n} + \frac{1}{m} }$ such that $n,m \in N$ and $p$ is prime [duplicate]
Let $p$ be a prime and let $n$ be a natural number such that $n \gt a$ .
Prove that $a|p+1$ if and only if exists integers $n,m$
Such that ${\frac{a}{p} = \frac{1}{n} + \frac{1}{m}}$
- 9
0
votes
1
answer
41
views
How many numbers between 1 and 1,000 (both inclusive) are divisible by at least one of the prime between 1 to 50? How can I find this? [closed]
I was trying to solve a compettive programming problem in which constraints are so high so I want to deduce a formula for it so that i could do it for other ranges as well.
8
votes
1
answer
635
views
How many integers are there that are not divisible by any prime larger than 20 and not divisible by the square of any prime?
I tackled the problem in the following way but i'm not sure if i'm correct.
I need the count of the numbers that have in their prime factorization only primes p such that $p \lt 20$ and those ...
1
vote
0
answers
181
views
Question about Zeta-distribution regarding divisibility by primes
For $s>1$ the Riemann Zeta-function is $$\zeta(s)=\sum_{n=1}^{\infty}n^{-s}$$
For a random variable $X$ with values in $\Bbb{N}$, its distribution is given by
$$\Bbb{P}[X=n]=\frac{n^{-s}}{\zeta(s)...
- 2,469
0
votes
1
answer
196
views
Calculate all prime numbers $x$, where $x^{18} - 1$ is divisible by $28728$
Question: Calculate all prime numbers $x$, where $x^{18} - 1$ is divisible by $28728$
Apparently, the answer is all prime numbers except $2, 3, 7,$ and $19.$ I did some prime factorisation and found ...
- 315
5
votes
1
answer
195
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Find all $n$ such that $n/d(n) = p$, a prime, where $d(n)$ is the number of positive divisors of $n$
Let $d(n)$ denote the number of positive divisors of $n$. Find all $n$ such that $n/d(n) = p$, a prime.
I tried this, but only I could get two solutions.
I proceeded like this -
Suppose
$$n = p^r \...
user636268
0
votes
1
answer
477
views
Find numbers with n-divisors in a given range
I'm trying to answer this question.
Are there positive integers $\le200$ which have exactly 13 positive divisors? What about 14 divisors? If yes, write them. If no, explain why not.
Because I'm ...
user432382
1
vote
1
answer
102
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Checking if the Product of n Integers is Divisible by Prime N
Given $n$ integers, $x_1, ... , x_n$, is there some well-known procedure or algorithm that checks if the product $x_1 * ... * x_n$ is divisible by some arbitrary prime $N$ using minimal space?
Since ...
- 315
3
votes
3
answers
185
views
Divisors of $\left(p^2+1\right)^2$ congruent to $1 \bmod p$, where $p$ is prime
Let $p>3$ be a prime number. How to prove that $\left(p^2+1\right)^2$ has no divisors congruent to $1 \bmod p$, except the trivial ones $1$, $p^2+1$, and $\left(p^2+1\right)^2$?
When $p=3$, you ...
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