New answers tagged prime-factorization
-1
votes
Is there a more efficient way to find the least prime factor?
For a general number $n$, the fastest known way to find the smallest prime number of $n$ is to use ECM factoring. This is fairly efficient if there exists a small factor, but can take an extremely ...
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-1
votes
Is there a more efficient way to find the least prime factor?
You can reverse the task and get some information. For any prime $p$ you can compute $n\# + 1 \pmod p$ without tears.
Let's see, a big loop on primes $p$ up to some bound. A list of the ...
- 141k
2
votes
Find sum of factorials divisible by the largest possible prime squared
I used such approach:
for given $n$ (currently, $n=32$), loop through prime numbers $p$ starting from certain value $p_0$ to, theoretically, $\sqrt{\sum_{k=1}^n k!}$;
and for these $(n,p)$ construct 2 ...
- 17.4k
3
votes
Smallest "diamond-number" above some power of ten?
The smallest "diamond-number" (if my calculations are correct), related to $10^{37}$, is
$$
10^{37} + 1483238923930317 = 1102689419521^2 \times 8224198521037.
$$
The smallest "diamond-...
- 17.4k
0
votes
Computing the radical of an integer's equality
Generalising on Peter's comment, I don't think there is an 'efficient' (polynomial time) way to confirm that an arbitrary candidate integer m is the radical of an arbitrary integer n, but if you know ...
- 261
2
votes
Accepted
Does the monoid of non-zero representations with the tensor product admit unique factorization?
Counterexamples are much easier to produce than this and exist already when $G = C_2$ and with two $2$-dimensional representations, see here.
Abstractly the problem is that the representation ring is ...
- 432k
2
votes
Does the monoid of non-zero representations with the tensor product admit unique factorization?
A counterexample is given by Nate at https://math.stackexchange.com/a/4436073/491450 :
Taking $G = A_5$, we have
$$
V_4 \otimes V_5 \otimes V_3 \cong V_4 \otimes V_5 \otimes {V_3}'
$$
where the ...
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