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Results tagged with sums-of-squares
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user 2757
30
votes
Accepted
What's the probability that k + n^2 is squarefree, for fixed k?
More generally, suppose that $f(x) \in \mathbf{Z}[x]$ has no repeated factors. For each prime $p$, let $c_p$ be the number of integers $x \in \{0,1,\ldots,p^2-1\}$ satisfying $f(x) \equiv 0 \pmod{p^2 …
- 23.8k
48
votes
Intuition for the last step in Serre's proof of the three-squares theorem
A few days ago Serre told me about some modest improvements to the proof, based on Weil's book Number theory: an approach through history from Hammurapi to Legendre and on a 1998 letter from Deligne t …
- 23.8k