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Mohsen Shahriari's user avatar
Mohsen Shahriari's user avatar
Mohsen Shahriari's user avatar
Mohsen Shahriari
  • Member for 9 years, 1 month
  • Last seen this week
  • Tehran, Iran
35 votes
Accepted

Why do we do mathematical induction only for positive whole numbers?

9 votes
Accepted

Parallelogram law functional equation: $ f ( x + y ) + f ( x - y ) = 2 \big( f ( x ) + f ( y ) \big) $

8 votes
Accepted

d'Alembert functional equation: $f(x+y)+f(x-y)=2f(x)f(y)$

6 votes
Accepted

(Non-continuous) solutions to $f\big(f(x)\big)=kx$ and $f\left(x^2\right)=xf(x)$

6 votes
Accepted

Solution to the functional equation $f(x^y)=f(x)^{f(y)}$

5 votes
Accepted

Giving tight asymptotic bounds for $ T ( n ) = T \left( \frac n { \log n } \right) + \log \log n $

5 votes

When does this equation have a solutions in integers: $ z ^ x + \bar z ^ y = 1 $?

5 votes

How to prove $f(x)=ax$ if $f(x+y)=f(x)+f(y)$ and $f$ is locally integrable

5 votes
Accepted

Cauchy's functional equation with bounds: $ a \le f ( x ) + f ( y ) - f ( x + y ) \le b $

5 votes
Accepted

$f(xy + x +y) = f(xy) + f(x) + f(y)$ and $f(x)(y - x) + f(y)(x - y) \geq 0$.

5 votes
Accepted

If $g(x+y)\le2\cdot\max\{g(x),g(y)\}$ and $g(xy)=g(x)g(y)$, show that $g(x+y)\le g(x)+g(y)$.

5 votes
Accepted

Solving the functional equation: $f\bigl(f(x)-x\bigr)=2x$

4 votes

Let $f:\mathbb N\to \mathbb N\;$ be a strictly increasing function s.t. $\;f\bigl(f(n)\bigr)=3n$ for all $n$. Find $f(2001)$ via a specific approach

4 votes
Accepted

Functional inequality $\sqrt{f(x+y)}\leqslant\sqrt{f(x)}+\sqrt{f(y)}$

4 votes
Accepted

Can the derivative difference be arbitrarily larger than the function difference?

4 votes

How to strengthen $ h \big( 2 h ( x ) \big) = h ( x ) + x $ to force $ h $ to be linear?

4 votes
Accepted

Does there exist such a function $f(x)$ that $f^n(x)=\left (1-\frac {1}{\sqrt[n]{x}} \right)^n?$

4 votes
Accepted

Solving the equation: $ f ( n ) = \left \lfloor \frac n 2 \right \rfloor $

4 votes

Solving a functional equation: $f\left(x^{f(y)}\right)=f(x)^{y}$ for all positive $x$ and $y$.

4 votes

solving functional equation $f(x+y) +f(x)f(y)=f(x)+f(y)+f(xy)$ for all real numbers

4 votes

d'Alembert-like functional equation: $f(x+y)+g(x-y)=\lambda f(x)g(y)$

4 votes
Accepted

Functional equation $f(x+y)-f(x)-f(y)=\alpha\big(f(xy)-f(x)f(y)\big)$ is solvable without regularity conditions

4 votes

Proof of a sum with binomial coefficients $\sum_{k=1}^n (-1)^{k+1}{\binom nk}\frac{1}{k} = 1 + \frac{1}{2} + \ldots +\frac{1}{n}$

4 votes
Accepted

Find a (closed) defining formula for XOR

4 votes
Accepted

How to read 4th order mixed Leibniz derivative

4 votes

Is squared Euclidean distance a metric?

4 votes

Functional equation involving sine function: $ \sin x + f ( x ) = \sqrt 2 f \left( x - \frac \pi 4 \right) $

4 votes
Accepted

Is the finite sum of factorials constant modulo the summation limit?

4 votes
Accepted

Functional Equation: $f \left(x+\cos(2017y) \right)=f(x)+2017\cos\left(f(y)\right)$

3 votes

Find all functions $f:\mathbb R \rightarrow \mathbb R$, such that: $(x^2 − y^2)\cdot f(xy) = x\cdot f(x^2y) − y\cdot f(xy^2)$

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