Polynomial (possibly a multivariate polynomial) with integer coefficients.

Sometimes systems of Diophantine equations are considered.

Problems generally involve finding integer solutions to the equations, notably determining if any solution exists, and if infinitely solutions exist.

The general problem is known to be undecidable: Hilbert's tenth problem.

The Pythagorean triples, and its generalization Fermat's last theorem, are the quintessential examples.

Direct consequence of Euclid's formula.

A generalization of the Pythagorean triple infinity question.

Once you hear about the uncomputability of such problems, it makes you see that all Diophantine equation questions risk being undecidable, though in some simpler cases we manage to come up with answers. The feeling is similar to watching people trying to solve the Halting problem, e.g. in the effort to determine BB(5).

Daniel S. Weld is a prominent computer scientist known for his work in artificial intelligence, particularly in areas such as knowledge representation, reasoning, and machine learning. He has made significant contributions to the development of AI systems and has been involved in research that explores how machines can simulate aspects of human reasoning and decision-making. Weld is a professor at the Paul G. Allen School of Computer Science & Engineering at the University of Washington, where he has conducted extensive research and taught courses related to AI.

Fred Pollack is an American poet known for his influential work in contemporary poetry. He is particularly recognized for his innovative use of form and style, often experimenting with narrative and structure in his poems. Pollack gained notable attention for his collection titled "The Adventures of Mr. H." and has published several other poetry collections, essays, and critical writings. In addition to his creative work, Pollack has also been involved in academia, teaching creative writing and literature.

Fredrik Liljegren is a name that may refer to various individuals, but it is not widely recognized in popular media or public figures as of my last knowledge update in October 2023. If you are referring to a specific person, it would be helpful to provide more context or details, such as their profession or any notable achievements.

As of my last knowledge update in October 2023, George Radin does not appear to be a widely recognized figure, concept, or entity. It's possible that he could be a private individual, a minor public figure, or associated with specific professions or organizations that are not well-documented in mainstream sources.

James Aspnes is a computer scientist known for his contributions to the fields of distributed systems, algorithms, and game theory. He is a professor at Yale University and has published numerous papers on topics related to these areas. Aspnes has made significant advancements in the understanding of how distributed systems operate and how algorithms can be designed to efficiently solve problems in these systems.

As of my last knowledge update in October 2021, there is no widely recognized figure or concept named "John van Geen." It's possible that you may be referring to a relatively obscure individual, a misspelling, or a new figure or concept that has emerged after my training data.

"Jie Lu" could refer to different subjects depending on the context. It could be a name, possibly referring to a person in academia, business, or another field. In Chinese, "Jie" (杰) can mean "outstanding" or "heroic," and "Lu" (璐) often means "jade" or "beautiful stone.

Jonathan Shewchuk is a notable figure in the field of computer science, particularly recognized for his contributions to computational geometry and numerical methods. He is known for developing algorithms related to polygonal mesh generation and has also worked on various aspects of mesh processing. His research work often focuses on applications in computer graphics, computer-aided design, and finite element analysis.

As of my last knowledge update in October 2023, there is no widely recognized individual or concept known as "Joseph Seffi Naor." It’s possible that he is a private individual, a lesser-known figure, or a recent personality who gained prominence after that date.

Kees van Prooijen is a Dutch social psychologist known for his research in the fields of social psychology, conspiracy theories, and the psychology of power and social influence. He has published numerous academic articles and has contributed to the understanding of how social processes shape beliefs and behaviors, particularly in the context of societal challenges and crises.