tarit goswami's user avatar
tarit goswami's user avatar
tarit goswami's user avatar
tarit goswami
  • Member for 5 years, 8 months
  • Last seen more than a month ago
  • India
19 votes

Produce an explicit bijection between rationals and naturals

11 votes

Is there much benefit in memorising proofs outside of an exam setting?

11 votes

How to attack "if true, prove it; if not true, give a counterexample" question?

10 votes

Calculate $\sum_{n\ge2}\log\left(1-\frac1{n^2}\right)$

7 votes

Can an integer of a particular form be a perfect square?

6 votes

A tricky combinatorial sum

5 votes

How to manipulate the given sum using Snake Oil method?

5 votes

(Combinatorial?) Proof of the identity $\sum_{k=1}^n \frac {(-1)^k}{k\,(k+1)}\binom nk = \frac 12 + \frac 13 + \dots + \frac 1{n+1}$?

5 votes

Twin primes whose sum is a cube

5 votes
Accepted

Find the shortest path from a point to curve

5 votes
Accepted

$4^x + 5^x = 6^x$

5 votes
Accepted

Proof that $\frac{1 + \sqrt{5}}{2}$ is irrational.

5 votes

Solving Trigonometric Questions Without a Calculator

4 votes
Accepted

Prove $\frac{a^2}{3^3}+\frac{b^2}{4^3}+\frac{c^2}{5^3} \ge \frac{(a+b+c)^2}{6^3}$

4 votes
Accepted

Proving inequality $x\ln(x)+y\ln(y)\geq(x+y)\ln(\frac{x+y}{2})$

4 votes
Accepted

If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$

3 votes
Accepted

Replacing $b$ with $bi$ in $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ turns the ellipse equation into a hyperbola equation; is there a deep meaning to this?

3 votes
Accepted

Prove the midpoint formula using only the vector space axioms.

3 votes

How to find the $\pi$?

3 votes

Find $\lim\limits_{x\to 0}\left (\frac{1^x+2^x+3^x+\dots+n^x}{n} \right)^{\frac1x}$

3 votes
Accepted

How do I know that $n \neq k^3$ if $n, k$ are natural numbers and $n$ has exactly 999 divisors?

3 votes
Accepted

Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.

3 votes
Accepted

Prove two numbers are coprime

3 votes

$x_1 x_2 x_3 x_4 + x_2 x_3 x_4 x_5 +......+ x_n x_1 x_2 x_3 = 0$ then what is $n$?

2 votes
Accepted

Help with proof that if q is a prime divisor of $\frac{n^p-1}{n-1}$, then either q=p or $q\equiv1 \pmod p$

2 votes

$f:[a,b]\rightarrow [c,d]$ be monotone and bijective. If $b-a>d-c$ can we say that function is decreasing.

2 votes

Number Theory Puzzle: Competition Problem

2 votes

Find all f such that $f(f(y))+f(x-y)=f(xf(y)-x)$

2 votes

Why is this relation antisymmetric?

2 votes

Is a polynomial of degree 3 with irrational roots possible?