#diophantine — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #diophantine, aggregated by home.social.
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🚀 Ah, the age-old question: how many API calls can you squeeze into an hour using quadratic equations and pure ✨wizardry✨? Because obviously, when facing a straightforward 10 requests per hour limit, the only logical step is to consult your dusty #Diophantine tome and channel your inner #Pythagoras 🤓🔢. Forget practical solutions; let's dive into the mathematical abyss for fun! 😂📉
https://vivekn.dev/blog/rate-limit-diophantine #APIcalls #QuadraticEquations #MathHumor #HackerNews #ngated -
It's well known you can find a solution to the linear Diophantine equation
\[ a_1x_1 + a_2x_2 + \ldots + a_nx_n = c \]
in polynomial time using the Extended Euclidean Algorithm. But I haven't been able to find a clear answer for the complexity of finding a non-negative integer solution, that is, \( x_i \geq 0 \).
The unbounded knapsack problem is NP-complete, and this is the case where the weights and costs are equal, but I'm not sure that the NP-hardness reduction applies given that additional constraint.
I have also found a statement that the "multidimensional knapsack problem" is NP-hard even with a single row, which seems to match this, but I lack a copy of Papadimitriou and Steiglitz to verify that statement, and can't figure out the reduction.
If this problem is NP-hard, then I'm also interested in showing that a related problem is also NP-hard: if we have one non-negative solution, can we find a second one? I'm trying to answer a question about the special case \( c = \sum_{i=1}^{n} a_i \).
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If I'm really committed to the fact that there is no such thing as actual infinity - and I am: https://www.wisdomneverdies.com/blog/no-infinity -
then there are no actual irrational numbers. By Kronecker's Theorem then, all apparently chaotic behavior is ultimately periodic. An interesting corollary 🙂#infinity #math #philosophy #Cavendish #Cantor #Locke #Aristotle #Knuth #chaos #Kronecker #Diophantine
