13,435 reputation
1653
bio website matemate.it
location Pisa, Italy
age
visits member for 1 year, 9 months
seen 14 hours ago

I received a master's degree after studying at the University of Pisa and I am attending my PhD at the University of Parma, Italy. I work in analytic number theory, and always had the spot for real analysis, special functions, (analytic) combinatorics and euclidean geometry.

I am the webmaster of www.matemate.it.


14h
comment Find a coset $f (= f + 22\Bbb Z)$ so that $(\Bbb Z/22\Bbb Z)^\times=U_{22} = \langle f\rangle$.
@PVAL: yes, you are clearly right. Since we know that $3$ is not a primitive element, the hunt for the primitive element continue on $\mathbb{Z}_{/22\mathbb{Z}}^*\setminus\langle 3\rangle$, hence $7$ is the next natural candidate, we do not need to pass through $5=3^3$.
14h
revised Find a coset $f (= f + 22\Bbb Z)$ so that $(\Bbb Z/22\Bbb Z)^\times=U_{22} = \langle f\rangle$.
edited body
14h
reviewed Leave Open Evaluate the limit $\lim \limits_{x \to \infty} \frac{1}{x(x+1)}$
15h
comment How to show that $\Phi(1-x)^{-1} =O(\sqrt{\log{x^{-1}}})$
@user165795: I politely ask you to accept my answer, if you think it is satisfactory.
15h
comment Finding $\binom{n}{0} + \binom{n}{3} + \binom{n}{6} + \ldots $
and this question: math.stackexchange.com/questions/868695/… is an almost duplicate.
15h
comment Find $\lim_{n \rightarrow \infty}$$\int_0^n(1 + \frac{-x}{n})^n\cos(\frac{x}{\sqrt{n}})e^{x/2}dx$
It is the Bernoulli inequality: for any $x$ such that $|x|\leq n$, $\left(1+\frac{x}{n}\right)^n\leq e^x.$ It just follows from the concavity of the logarithm.
15h
reviewed Leave Open Find a coset $f (= f + 22\Bbb Z)$ so that $(\Bbb Z/22\Bbb Z)^\times=U_{22} = \langle f\rangle$.
15h
answered Find a coset $f (= f + 22\Bbb Z)$ so that $(\Bbb Z/22\Bbb Z)^\times=U_{22} = \langle f\rangle$.
15h
reviewed Close BINOMIAL PMF distribution
15h
reviewed Close Write the particular equation…Predict her speed
15h
reviewed Leave Open Using joint probability density function to find the conditional probability of an event
15h
reviewed Edit An arithmetic sequence whose members do not contain the digit ‘9’
15h
revised An arithmetic sequence whose members do not contain the digit ‘9’
added 12 characters in body
15h
reviewed Close Curve sketching from derivative to the original
15h
comment Find $\lim_{n \rightarrow \infty}$$\int_0^n(1 + \frac{-x}{n})^n\cos(\frac{x}{\sqrt{n}})e^{x/2}dx$
$(1-\frac{x}{n})^n\leq e^{-x}$.
15h
comment An arithmetic sequence whose members do not contain the digit ‘9’
If now we consider the subsequence given by the terms with an even index, we see that the only chance for the step is to be $\equiv 25\pmod{100}$, and we can finish by enumerating all the cases $100x+25\pmod{1000}$ in order to avoid the residue classes $900+[0,99]\pmod{1000}$, and check that we cannot have more than $72$ terms like in the $125m+1$ case.
15h
comment An arithmetic sequence whose members do not contain the digit ‘9’
Now, if the step is $\equiv 5,15,35,75,95\pmod{100}$ we have at most $20$ terms. Hence we have that the step must be $\equiv 25,45,65,85\pmod{100}$.
15h
comment An arithmetic sequence whose members do not contain the digit ‘9’
For first, if the step (i.e. the difference of two consecutive terms in the sequence) is $\equiv 1,3,7,9\pmod{10}$ the sequence cannot have more than $10$ terms since we fall soon into the residue class $9\pmod{10}$. We must also avoid to fall soon into the residue classes $90+[0,9]\pmod{100}$, hence the only choice is to have a step $\equiv 5\pmod{10}$, otherwise we have at most $44$ terms.
16h
revised An arithmetic sequence whose members do not contain the digit ‘9’
added 17 characters in body
17h
comment How is $ \sum_{n=1}^{\infty}\left(\psi(\alpha n)-\log(\alpha n)+\frac{1}{2\alpha n}\right)$ when $\alpha$ is great?
@OlivierOloa: Ok, that was not so hard, just a consequence of $f(x)\geq x/12$, done.