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Inceptio
  • Member for 11 years, 3 months
  • Last seen more than 6 years ago
13 votes
5 answers
2k views

Prove that there are infinitely many natural numbers $n$, such that $n(n+1)$ can be expressed as sum of two positive squares in two distinct ways.

11 votes
4 answers
3k views

Proof of Wolstenholme's theorem

10 votes
2 answers
284 views

Show that there are infinitely many solutions of distinct natural numbers $m,n$ such that $n^3+m^2\mid m^3+n^2$

9 votes
4 answers
1k views

Solutions to $p+1=2n^2$ and $p^2+1=2m^2$ in Natural numbers.

9 votes
2 answers
4k views

Let $p$ be an odd prime number. How many $p$-element subsets of $\{1,2,3,4, \ldots, 2p\}$ have sums divisible by $p$?

8 votes
4 answers
1k views

Evaluate $\int _0 ^ \pi \frac{x}{1+\sin^2(x)} dx $

7 votes
4 answers
388 views

Polynomials Question: Proving $a=b=c$.

6 votes
2 answers
222 views

If the permuted set of $(1,2, \dots n ) $ is such that sum of any two adjacent numbers is a square. Find the generalized form of $n$.

4 votes
2 answers
1k views

Factorials and Arithmetic Progression.

2 votes
3 answers
132 views

Constrictions on A.P with factorials.

2 votes
0 answers
158 views

Existence of closed form solutions on a definite integral.

2 votes
1 answer
2k views

The minimum number of mice required to find a poisoned bottle.

2 votes
0 answers
139 views

Are there infinitely many primes $p_k$ such that $(p_k-1)!+p_k$ is a also prime?

2 votes
0 answers
134 views

Finding the sum of non-real roots of a polynomial.

1 vote
1 answer
305 views

Article about primes.(Revised)