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Vidyanshu Mishra's user avatar
Vidyanshu Mishra's user avatar
Vidyanshu Mishra's user avatar
Vidyanshu Mishra
  • Member for 7 years, 10 months
  • Last seen more than 1 year ago
34 votes
7 answers
6k views

What is the role of conjectures in modern mathematics?

15 votes
2 answers
3k views

Are there infinitely many Mama's numbers and no Papa's numbers?

13 votes
5 answers
403 views

Show that $e^n>\frac{(n+1)^n}{n!}$ without using induction.

12 votes
6 answers
2k views

What is wrong with the "proof" for $\ln(2) =\frac{1}{2}\ln(2)$?

11 votes
2 answers
5k views

$\frac{1}{e}=$"Probability that every chocolate goes into a wrong spot".

11 votes
2 answers
781 views

Please verify my proof of: There is no integer $\geq2$ sum of squares of whose digits equal the integer itself.

9 votes
6 answers
3k views

Find all numbers such that "Product of all divisors=cube of number".

9 votes
1 answer
146 views

Find all real functions $f:\mathbf{R} \to \mathbf{R}$ satisfying the relation $f(x^2+y(f(x)))=x(f(x+y))$.

8 votes
10 answers
499 views

How can I derive what is $1\cdot 2\cdot 3\cdot 4 + 2\cdot 3\cdot 4\cdot 5+ 3\cdot 4\cdot 5\cdot 6+\cdots + (n-3)(n-2)(n-1)(n)$ ??

7 votes
1 answer
269 views

Show that the equation $\sqrt{ax+\alpha}+\sqrt{bx+\beta}+\sqrt{cx+\gamma}=0$ reduces to a simple equation.

7 votes
5 answers
2k views

How does one get that $1^3+2^3+3^3+4^3+\cdots=\frac{1}{120}$? [duplicate]

6 votes
3 answers
359 views

The smallest odd perfect number must exceed $10^{300}$.

6 votes
1 answer
320 views

Are there infinitely many primes with digit sums of the form $n^2+1$?

5 votes
4 answers
338 views

What is the reason for saying that mathematics does not constitute science even if use experimental approach so often in mathematics? [closed]

5 votes
3 answers
131 views

What really is the difference between $\mathbf{v}=(2,3) $ and $\mathbf{u}=(2,3,0)$?

5 votes
1 answer
148 views

Find all function $ f:\Bbb R\to\Bbb R$ such that $ f(x+y)f(x-y)=(f(x)+f(y))^2-4x^2f(y)$.

5 votes
4 answers
153 views

How can $\frac{x^3-4x^2+4x}{x^2-4}$ be both $0$ and "undefined" when $x = 2$?

4 votes
3 answers
2k views

Show that equation $x^2+y^2+z^2=(x-y)(y-z)(z-x)$ has infinitely many solutions in integers $x,y,z$

4 votes
2 answers
2k views

Problem in solving this book and pages question

4 votes
1 answer
156 views

Finding existence of $ f : N → N $ with the following properties: $f(1) = 2$ and $f(f(n)) = f(n)+n (n ∈ N).$

4 votes
2 answers
122 views

Compute $\frac{p(12)+p(-8)}{10}$ where $p(x)=x^4+ax^3+bx^2+cx+d$

3 votes
2 answers
185 views

Finding $26$th digit of a number.

3 votes
1 answer
184 views

Olympiad level assignment problem having a use of geometry and trigonometry.

3 votes
2 answers
238 views

Centre of symmetry of a bound figure.

3 votes
2 answers
356 views

Interesting identities/formulae/results involving Fibonacci numbers. [closed]

3 votes
1 answer
708 views

Product of $10$ consecutive integers can never be a perfect square

2 votes
1 answer
315 views

Find all integer $(a,b,c)$ such that $ab+bc+ca=abc$.

2 votes
5 answers
27k views

How to relate areas of circle, square, rectangle and triangle if they have same perimeter??

2 votes
2 answers
3k views

What is the significance of the zero vector?

2 votes
4 answers
3k views

What is the role of associative and commutative properties in Mathematics and what if someone want to prove them??