0
votes
0answers
30 views

Differential Diophantine Equations?

So this is both a question on its own as well as a request for where I can find information on a given topic. Consider Differential Equations in two variables of the form: $$P(Z,Z', Z'' ... Z^{[n]}, ...
7
votes
1answer
114 views

All functions $g:\mathbb{N}\to\mathbb{Z}$ such that $m+n~|~g(m)+g(n)$

I just thought about the following question: Find all functions $g:\mathbb{N}\to\mathbb{Z}$ such that $m+n~|~g(m)+g(n)$ for all $m,n\in\mathbb{N}$. Clearly every polynomial $g(X)\in\mathbb{Z}[X]$ in ...
-1
votes
2answers
67 views

Context problems of Number theory and functional equation

I can't solve the following problems, please help. 1) Find all primes $p$ and $q$ such that $p^q+q^p$ is a prime. 2) Solve $2^x+3^y=z^2$ in integers. 3) Find all $f: \mathbb{Q} \rightarrow ...
1
vote
3answers
77 views

Looking for an equation

This is kind of a reverse question. A few years back I was presented with a functional equation problem, I don't remember it completely, and now I would appreciate the help of the math.SE hivemind to ...
1
vote
0answers
108 views

where can I find a good Proof for Cauchy's functional equation

Do you know where can I find good proofs for Cauchy's functional equation?