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Shubhrajit Bhattacharya
  • Member for 5 years
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20 votes
Accepted

Is it possible that $2^{2A}+2^{2B}$ is a square number?

16 votes

Polynomial outputs containing a particular Integer sequence

14 votes

Book recommendation : Olympiad Combinatorics book

7 votes

Find the roots of all cubics $f(x)$ given $f(2)=1$ and all roots are integral

6 votes

When is $-3$ a quadratic residue mod $p$?

6 votes

what points make $\frac{1}{x} + \frac{1}{y} = \frac{1}{n}$ true?

5 votes

Some Combinatorics and Some Prime Numbers

5 votes
Accepted

Find all positive integers $n$ such that $\varphi(n)$ divides $n^2 + 3$

5 votes
Accepted

We have $a,b,c$ and $d$ are real numbers such that $\frac{b + c + d}{a} = \frac{a + c + d}{b} = \frac{a + b + d}{c} = \frac{a + b + c}{d} = r$.

5 votes
Accepted

Does $\Phi_n(\alpha)=0$ in $\Bbb{F}_p$ for some $\alpha\in\mathbb{F}_p$ imply that $\mathrm{ord}_p(\alpha) = n$?

5 votes
Accepted

Prove that $\sum _{x=0}^{p-1}e^{\frac {2\pi ix^{2}}{p}}={\sqrt {p}} $ , $ p \equiv 1{\pmod {4}}$

5 votes
Accepted

How can I prove this inequality using HM-GM-AM-QM inequalities?

4 votes

For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$

4 votes
Accepted

How to calculate $ \sum_{n=0}^{\infty}\frac{x^{2}}{\left(1+x^{2}\right)^{n}} $

4 votes

If $abc=1$ and $a,b,c$ are positive real numbers, prove that ${1 \over a+b+1} + {1 \over b+c+1} + {1 \over c+a+1} \le 1$.

4 votes

How to show $n=1+\sum_{k=1}^{n}\left\lfloor{\log_2\frac{2n-1}{2k-1}}\right\rfloor$ for every natural number $n$.

4 votes
Accepted

EGMO 2014/P3 : Prove that there exist infinitely many positive integers $n$ such that $\omega(n) = k$ and $d(n)$ does not divide $d(a^2+b^2)$

4 votes

INMO : Prove that $\sqrt[3]{a}$ and $\sqrt[3] {b}$ themselves are rational numbers

4 votes
Accepted

USA TST 2018/P1: Prove that the $n^{\text{th}}$ smallest positive integer relatively prime to $n$ is at least $\sigma(n)$

4 votes
Accepted

Power series expansion of a product of two power series representations

3 votes

Polynomial outputs containing a particular Integer sequence

3 votes
Accepted

Show that $\lvert \lvert (x,y) \rvert \rvert \rightarrow \infty$ implies $f(x,y) = x^2-4xy+4y^2+y^4-2y^3+y^2 \rightarrow \infty$

3 votes

Prove that there are at least $2005$ pairs of $(x, y)$ of non negative integers x and y that satisfy $x^2+y^2 = N,$ for some positive integer $N$.

3 votes

If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational

3 votes

$p$-adic Numbers Textbook Suggestions

3 votes
Accepted

Proof by contradiction of a variant of PHP

3 votes
Accepted

Number of binomial coefficients among $\binom{n}{k}\;(0\leq k\leq n)$ which are divisible by $p$, where $n = (n_mn_{m - 1}...n_0)_p$ in base $p$

3 votes

Functions satisfying $f(x)f(y)=2f(x+yf(x))$ over the positive reals

3 votes
Accepted

Show that the sequence $a_n=\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{n}$ is rising and is unbounded.

3 votes

How to prove Gaussian Integers is a UFD Formally