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CryoDrakon
  • Member for 9 years, 3 months
  • Last seen this week
  • Dortmund, Germany
12 votes
3 answers
291 views

Prove that $a+b$ can't divide $a^a+b^b$ nor $a^b+b^a$

10 votes
2 answers
872 views

Proving the inequality $4\ge a^2b+b^2c+c^2a+abc$

8 votes
2 answers
3k views

Solve the following functional equation $f(xf(y))+f(yf(x))=2xy$

8 votes
3 answers
253 views

Closed form of $\int\limits_0^{2\pi} \prod\limits_{j=1}^n \cos(jx)dx$ and combinatorial link

7 votes
3 answers
132 views

Find all $n$ so that $s(2^n)=s(5^n)$

6 votes
2 answers
846 views

Solve $3^a-5^b=2$ for integers a and b.

6 votes
3 answers
903 views

Prove the following inequality $\sqrt[n]{x_1x_2...x_n}\ge (n-1)$

6 votes
1 answer
169 views

Show that for $n$ distinct numbers the following holds

6 votes
1 answer
109 views

Prove that one of the elements can't be in the interval $(0,1)$

5 votes
0 answers
203 views

Find all $x,y\in \mathbb{N}$ such that: $2^x+17=y^2$.

5 votes
2 answers
462 views

Solve functional equation $(x+y)(f(x)-f(y))=f(x^2)-f(y^2)$ [duplicate]

4 votes
3 answers
238 views

Solve $\sin \frac{\alpha - \beta}2 + \sin \frac{\alpha - \gamma}2 + \sin \frac{3\alpha}2 =\frac 3 2$

4 votes
2 answers
133 views

Prove that the sequence $p_i$ is bounded

4 votes
2 answers
212 views

Prove that $\angle DAP=\angle CAB$ in a parallelogram $ABCD$

4 votes
2 answers
168 views

Proving the inequality $\frac{9}4\ + \frac{3abc}4\ \ge ab+bc+ca$

4 votes
3 answers
131 views

Prove the inequality $4+xy+yz+zx \ge 7xyz$

4 votes
0 answers
167 views

Prove the inequality for all positive real numbers $a,b,c,p$

4 votes
2 answers
274 views

Prove that the circle which contains ATB and incircle of ABC touch in one point(T).

4 votes
2 answers
184 views

Find all real functions so that $f(xf(y)+f(x))=f(yf(x))+x$

3 votes
2 answers
58 views

Find all positive integers $(a,b)$ so that $p_a-p_b\mid 2(a-b)$

3 votes
3 answers
397 views

Solve the following functional equation: $[f(x)+f(y)][f(x+2y)+f(y)]=[f(x+y)]^2+f(2y)f(y)$

3 votes
1 answer
545 views

All triangles are equilateral

3 votes
5 answers
599 views

Prove that the sum is always greater than $1$

3 votes
1 answer
489 views

Find all real functions $f$ such that $f(xf(y))=(1-y)f(xy)+x^2y^2f(y)$

3 votes
2 answers
322 views

Prove the following limits without using l'Hospital and Sandwich theorem

3 votes
1 answer
188 views

Multiple of $n$ and the sum of its digits is $k\geq n$.

3 votes
1 answer
232 views

Solve the eqation $a^3+2b^3+4c^3=6abc+1$

3 votes
3 answers
2k views

Solve the functional equation $f(xf(y)+x)=xy+f(x)$

3 votes
4 answers
1k views

Prove that $\int_{0}^{\infty} \sin(t^2)\,dt$ equals $\sqrt{\pi/8}$

3 votes
1 answer
102 views

Solve the non-linear differential equation