All Questions
Tagged with prime-factorization prime-numbers
831
questions
5
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What software can calculate the order of $b \mod p$, where $p$ is a large prime?
I wasn't sure where to ask this, but Mathematics seems better than StackOverflow or Programmers.
I have no background whatsoever in number theory, and I need to find software that can calculate the ...
- 191
1
vote
1
answer
98
views
Does $a \mid bc$ imply $\frac{a}{(a,b)} \mid c$?
If $a \mid bc$, then does $\frac{a}{(a,b)} \mid c$? I doubt anybody here is industrious enough to show this via a diagram, but who knows.
- 477
4
votes
1
answer
250
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Efficiency in factoring lists of consecutive numbers
Suppose I'm looking at prime factorizations of numbers in the vicinity of this one:
$$
1354 = 2 \times 677
$$
The smallest prime appears here, and the next prime after that does not.
Going one step ...
16
votes
6
answers
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prime divisor of $3n+2$ proof
I have to prove that any number of the form $3n+2$ has a prime factor of the form $3m+2$. Ive started the proof
I tried saying by the division algorithm the prime factor is either the form 3m,3m+1,3m+...
- 2,935
4
votes
3
answers
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About the factors of the product of prime numbers
If a number is a product of unique prime numbers, are the factors of this number the used unique prime numbers ONLY? Example: 6 = 2 x 3, 15 = 3 x 5. But I don't know for large numbers. I will be using ...
- 143
0
votes
1
answer
820
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Mean of highest exponent in prime factorization of all integers ≥ 2
For any natural number $n > 1$, define $E(n)$,to be the highest exponent to
which a prime divides it. For instance, $E(12)=E(36)=2$. Show that $$\lim_{N \to \infty} \frac{1}{N} \sum\limits_{n=2}^{N} E(...
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