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7
questions
1
vote
1
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49
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Generating function of partitions of $n$ in $k$ prime parts.
I have been looking for the function that generates the partitions of $n$ into $k$ parts of prime numbers (let's call it $Pi_k(n)$). For example: $Pi_3(9)=2$, since $9=5+2+2$ and $9=3+3+3$.
I know ...
1
vote
1
answer
289
views
Number of ways to write a positive integer as the sum of two coprime composites
I've recently learnt that every integer $n>210$ can be written as the sum of two coprime composites.
Similar to the totient function, is there any known function that works out the number of ways ...
- 103
0
votes
0
answers
51
views
Summation of a prime and a prime power
Is there an even number $n \in \mathbb{N}$ and two different primes $p,q<n$ which are not divisors of $n$, as well as $a,b \in \mathbb{N}$ with $a,b>1$, such that
$$
n=q+p^{a}=p+q^{b}
$$
? I ...
- 21
7
votes
1
answer
191
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Finding $z=x+y$ such that $x^2 + y^2$ is prime
For which integers $z$ can one write $z=x+y$ such that $x^2+y^2$ is prime?
It feels like it should be possible for all odd $z>1$, and I have tried to adapt Euler's proof of Girard/Fermat's ...
- 71
0
votes
1
answer
53
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Question about the partitions of a natural number
There is a function that counts the number of partitions of with $n$ digits?
I am aware of the partition function studied by Ramanujan, but what I want is a subset of the partitions that are counted ...
- 2,505
5
votes
1
answer
416
views
Existence of a prime partition
I'm interested in finding out whether there exists a prime partition of a given positive integer $N>1$ such that the partition has specific number of parts.
For instance, as given in another ...
- 51
1
vote
3
answers
625
views
Finite or infinite set?
Due to my not-so-advanced math skills, this question may take a few attempts to state clearly:
Consider the unordered pair (2-tuple) partitions of n (e.g. with n=4, we have {{4,0},{3,1},{2,2}}). ...
- 351