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visits member for 4 years, 2 months
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Nov
1
comment Half the rationals?
A good candidate for your set $X$ with a very simple description is the set of reduced fractions $a/b$ with $$ a\cdot b \equiv 0 \pmod{3} $$
Nov
1
comment Half the rationals?
I think there something missing in the right hand side of the inequality $\sum_{k=1}^{n-1} a_k\phi(k) < 1/2$, I suppose you mean $<\frac{1}{2}\sum_{k=1}^{n-1} \phi(k)$? On the other hand, even if it is probably true, I can't see how to prove that this construction works for all the intervals $Y$.
Nov
1
comment Half the rationals?
I think that the proportion of fractions with even numerator and denominator bounded by $N$ is aproximately one third, and the same for even denominator.
Oct
15
revised Tiling a minimal perimeter region with $n$ unit squares
Sketch of proof
Oct
15
answered Tiling a minimal perimeter region with $n$ unit squares
Jul
19
answered Solving a polynomial modulo an integer
Jun
8
awarded  Caucus
Apr
19
revised Burgess on quadratic residues and non-residues
edited body
Apr
19
comment Burgess on quadratic residues and non-residues
No that's an error I correct it
Apr
19
comment Burgess on quadratic residues and non-residues
I have edited the answer to make it more clear. I hope this helps.
Apr
19
revised Burgess on quadratic residues and non-residues
added 1406 characters in body
Apr
17
revised Burgess on quadratic residues and non-residues
correction
Apr
17
answered Burgess on quadratic residues and non-residues
Feb
21
revised Is it a bad idea to use a Sieve of Eratosthenes to find all primes up to very large N?
added 1962 characters in body
Feb
21
revised Is it a bad idea to use a Sieve of Eratosthenes to find all primes up to very large N?
added 1962 characters in body
Feb
21
answered Is it a bad idea to use a Sieve of Eratosthenes to find all primes up to very large N?
Dec
20
comment Consequence of Bertrand's Postulate
It proves that for every $N$ there exist a $k$ such that there are $N$ (or more) pairs of consecutive primes with common difference $k$. The problem if there are $N$ consecutive primes with common difference $k$ is AFAIK open, though is related to Green-Tao theorem.
Dec
19
comment Consequence of Bertrand's Postulate
user19012: It was my fault there was a flaw in the argument. I have corrected it.
Dec
19
revised Consequence of Bertrand's Postulate
Correction of an error in the argument
Dec
15
revised Consequence of Bertrand's Postulate
Clarification of the argument.