Linked Questions

13 votes
3 answers
3k views

Why are smooth numbers called "smooth"?

"Adleman refers to integers which factor completely into small primes as “smooth” numbers." (ME Hellman, JM Reyneri. Advances in Cryptology, 1983: citation link.) Does anyone know what is the ...
Joseph O'Rourke's user avatar
21 votes
2 answers
1k views

Most squares in the first half-interval

It is well known that if $p$ is an odd prime, exactly one half of the numbers $1, \dots, p-1$ are squares in $\mathbb{F}_p$. What is less obvious is that among these $(p-1)/2$ squares, at least one ...
Andrea Ferretti's user avatar
31 votes
1 answer
3k views

What was the error in the proof of Roos' theorem?

Background: In 1961, Roos (who, sadly, apparently passed away just last month) purported to prove [1] that in an abelian category with exact countable products (AB4${}^\ast_\omega$), limits of inverse ...
Tim Campion's user avatar
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9 votes
2 answers
1k views

On the definition of "almost-everywhere" for non-complete measure spaces

If $(X,\mathcal{B},\mu)$ is a (non-necessarily complete) measure space, we can give two different notions of a property $P(x)$ that is true almost-everywhere : (D1) There is a measurable set $A$ ...
Jon-S's user avatar
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