The following question is in particular reference to the previous question by Bjorn Poonen. I guess I won't even need to give this link, Polynomial representing all nonnegative integers, since this is perhaps the most famous question of MO until now.

I found this question interesting and natural as a curiosity. But from the interest of people, there seems to be more in it. (recall the exclamation What a nice problem! by Gil Kalai). May someone explain me why this question particularly interesting from, perhap, a number theorist perspective ? For example,is there some deeper linkage to other results ?

The same query applies to Fermat polygonal number theorem. Is there anything that these theorems reveal us about the deeper structure of integers?

More generally, I hope we can address the question: What is it that makes some diophantine equations interesting, while others are less so?

(The change was suggested by Kevin O'Bryant)

The following question is in particular reference to the previous question by Bjorn Poonen. I guess I won't even need to give this link, Polynomial representing all nonnegative integers, since this is perhaps the most famous question of MO until now.

I found this question interesting and natural as a curiosity. But from the interest of people, there seems to be more in it. (recall the exclamation What a nice problem! by Gil Kalai). May someone explain me why this question particularly interesting from, perhap, a number theorist perspective ? For example,is there some deeper linkage to other results ?

The same query applies to Fermat polygonal number theorem. Is there anything that these theorems reveal us about the deeper structure of integers?

More generally, I hope we can address the question: What is it that makes some diophantine equations interesting, while others are less so?

(The change was suggested by Kevin O'Bryant)

I guess I won't even need to give this link, Polynomial representing all nonnegative integers, since this is perhaps the most famous question of MO until now.

I found this question interesting and natural as a curiosity. But from the interest of people, there seems to be more in it. (recall the exclamation What a nice problem! by Gil Kalai). May someone explain me why this question particularly interesting from, perhap, a number theorist perspective ? For example,is there some deeper linkage to other results ?

The same query applies to Fermat polygonal number theorem. Is there anything that these theorems reveal us about the deeper structure of integers?

The following question is in particular reference to the previous question by Bjorn Poonen. I guess I won't even need to give this link, Polynomial representing all nonnegative integers, since this is perhaps the most famous question of MO until now.

I found this question interesting and natural as a curiosity. But from the interest of people, there seems to be more in it. (recall the exclamation What a nice problem! by Gil Kalai). May someone explain me why this question particularly interesting from, perhap, a number theorist perspective ? For example,is there some deeper linkage to other results ?

The same query applies to Fermat polygonal number theorem. Is there anything that these theorems reveal us about the deeper structure of integers?

More generally, I hope we can address the question: What is it that makes some diophantine equations interesting, while others are less so?

(The change was suggested by Kevin O'Bryant)

I guess I won't even need to give this link, Polynomial representing all nonnegative integers, since this is perhaps the most famous question of MO until now.

Yes, I agree that this is a very interesting and natural curiosity seeing the proof of Gauss and Lagrange. But may someone explain me why this question particularly interesting? (recall the exclamation What a nice problem! by Gil Kalai). Is there something deeper here? The same query applies to Fermat polygonal number theorem. Is there anything that these theorems reveal us about the deeper structure of integers?

I guess I won't even need to give this link, Polynomial representing all nonnegative integers, since this is perhaps the most famous question of MO until now.

I found this question interesting and natural as a curiosity. But from the interest of people, there seems to be more in it. (recall the exclamation What a nice problem! by Gil Kalai). May someone explain me why this question particularly interesting from, perhap, a number theorist perspective ? For example,is there some deeper linkage to other results ? 

The same query applies to Fermat polygonal number theorem. Is there anything that these theorems reveal us about the deeper structure of integers?