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Anurag A
  • Member for 9 years, 3 months
  • Last seen more than a week ago
  • USA
128 votes
Accepted

How to prove that all odd powers of two add one are multiples of three

27 votes

Conjecture: If $ N $ and $ N + 10 $ are prime, then $ N + 20 $ is composite.

27 votes
Accepted

Long limit question

26 votes
Accepted

Functions that are continuous only at two points?

21 votes

What does $\sum_{k=0}^\infty \frac{k}{2^k}$ converge to?

18 votes
Accepted

If $x$ and $y$ are not both $0$ then $ x^2 +xy +y^2> 0$

18 votes
Accepted

Show that any set in a metric space can be written as the intersection of open sets

17 votes

P is a natural number. 2P has 28 divisors and 3P has 30 divisors. How many divisors of 6P will be there?

16 votes
Accepted

Evaluate $\sum_{k=0}^{n} {n \choose k}{m \choose k}$ for a given $n$ and $m$.

14 votes

Is the set of all pairs of natural numbers countable?

14 votes

Why is $\mathbb{Z}[X]$ not a euclidean domain? What goes wrong with the degree function?

13 votes
Accepted

Group of order 10 has an element of order 5, without using Cauchy's or Sylow's theorems

13 votes
Accepted

Solve system of simultaneous equations in $3$ variables: $x+y+xy=19$, $y+z+yz=11$, $z+x+zx=14$

13 votes
Accepted

Show that the numbers $(2n + 1)$ and $(4n^2+1)$ are relatively prime

12 votes
Accepted

Remainder when $2005^{2002} + 2002^{2005}$ is divided by $2003$

12 votes

Dimension of a subspace defined by multiple restrictions.

11 votes

Solving the equation $\frac{\ln (x)}{\ln (1-x)} = \frac{1}{x} - 1$

11 votes

If $x^3 - 5x^2+ x=0$ then find the value of $\sqrt {x} + \dfrac {1}{\sqrt {x}}$

11 votes

A field has only one isomorphic subfield to itself?

11 votes

Computing a higher (2015) order partial derivative of $1/(x^2+y^2)$

10 votes

Number of integer solutions of $a^2+b^2=10c^2$

10 votes

If $G/Z(G)$ is abelian then $G$ is abelian?

10 votes
Accepted

Prove that the function $f$ is injective .

10 votes
Accepted

Question about inverse function $f(x)=\frac{1}{2}(x+\sqrt{x^2+4})$

10 votes
Accepted

The sides of a triangle are in Arithmetic progression

9 votes
Accepted

Problem in a Trigonometric Series

9 votes
Accepted

Any positive integer can be written as sum / difference of consecutive squares

9 votes
Accepted

what is the possible number of commutative binary operations that can be defined on a set of n elements?

9 votes
Accepted

Show $\frac{a^2}{b^2} + \frac{b^2}{a^2} +3 \ge 2\left(\frac{a}{b} + \frac{b}{a}\right)$

9 votes

Probability that $2^a+3^b+5^c$ is divisible by 4

1
2 3 4 5
45