User CryoDrakon

9 votes

Accepted

Let $p$ be a prime so $p\equiv3\pmod4$. If $p|a^2+b^2$, then $p|a,b$

answered Sep 16, 2016 at 19:41

4 votes

Accepted

Simplifying system of two-variable differential equations

answered Jan 23, 2018 at 14:02

4 votes

Accepted

Prove that primes of the form $2n^2+10n+15$ are also of the form $36k+7$

answered Feb 3, 2018 at 23:35

4 votes

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

answered Nov 18, 2014 at 13:29

4 votes

Accepted

Given that $n^4-4n^3+14n^2-20n+10$ is a perfect square, find all integers n that satisfy the condition

answered May 24, 2020 at 19:20

3 votes

Let $f(x)=x^{15}-2017x^{14}+2017x^{13}-2017x^{12}+2017x^{11}-...+2017x^{3}-2017x^{2}+2017x+2017$ What is $f(2016)?$

answered May 24, 2020 at 16:43

3 votes

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

answered Jan 7, 2015 at 15:39

3 votes

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

answered Jan 18, 2015 at 14:53

3 votes

Inequality with $a+b+c=1$

answered Sep 5, 2016 at 7:24

2 votes

If $f : \mathbb R \rightarrow \mathbb R $ such that $f(x^2+x)+2f(x^2-3x+2) = 9x^2-15x$. Find $f(2016)$.

answered Jun 14, 2018 at 9:22

2 votes

Accepted

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

answered Jan 7, 2015 at 12:36

2 votes

Area inside the astroid

answered Sep 4, 2016 at 16:35

2 votes

Where do I start learning Higher Mathematics?

answered May 9, 2016 at 18:38

2 votes

Negative Modulo confusion

answered Dec 12, 2014 at 21:28

2 votes

Accepted

In $\triangle ABC$, find the value of $\tan A\tan C$.

answered Dec 9, 2014 at 22:42

1 vote

Functional equation $f(a+b)^3-f(a)^3-f(b)^3=3f(a)f(b)f(a+b)$

answered Dec 11, 2014 at 16:03

1 vote

Accepted

Solve the equation $p^x-y^p=1$

answered Nov 19, 2014 at 14:18

1 vote

Prove that one of x,y,z is smaller than 3 and one is bigger than 5 if...

answered Nov 24, 2014 at 7:16

1 vote

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

answered Dec 24, 2014 at 4:16

1 vote

Find the value of k when $f(x) = x^3 -4x^2 + 6x + k$

answered Jun 14, 2016 at 19:32

1 vote

$p^n\mid ((p^{n-m}+1)^j-1)$?

answered Sep 16, 2016 at 21:44

1 vote

Accepted

Prove or disprove $\sum\limits_{cyc}\frac{x^4+y^4}{x+y}\le 3\frac{x^4+y^4+z^4}{x+y+z}$

answered Sep 19, 2016 at 14:10

1 vote

Prove that $a^x \equiv -1 \pmod{p}$ if and only if $k \mid 2x$ but $k \nmid x$

answered Oct 3, 2016 at 13:52

1 vote

Use mathematical induction to prove that $ \frac{(2n)!}{(2^n)} $ is a natural number for all n $\ge $ 0.

answered Sep 5, 2016 at 18:21

1 vote

Divisibility of a number of the form $3^{n}-1$

answered Jun 9, 2020 at 14:19

1 vote

Solving $y+\sqrt{y^2-1}=e^x$ respect to $y$

answered Nov 7 at 0:19

1 vote

Directed angles problem: For $A$, $B$, $C$ on $\bigcirc O$, show that $\angle OAC=90^\circ-\angle CBA$

answered May 24, 2020 at 22:26

1 vote

Accepted

Prove that for all $\alpha + \beta + \gamma = \pi$, $\sum_{cyc}\frac{\sin\beta}{\cos\beta + 1} = \frac{\sum_{cyc}\cos\beta + 3}{\sum_{cyc}\sin\beta}$.

answered May 22, 2020 at 22:17

1 vote

Accepted

Too many tangents

answered May 25, 2020 at 15:30

1 vote

Accepted

How to evaluate $\lim_{n \to \infty} \sqrt[n]{\frac{n^3}{2^n + 5^n}}$?

answered May 24, 2020 at 17:43

Stack Exchange Network

47 Answers

Let $p$ be a prime so $p\equiv3\pmod4$. If $p|a^2+b^2$, then $p|a,b$

Simplifying system of two-variable differential equations

Prove that primes of the form $2n^2+10n+15$ are also of the form $36k+7$

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

Given that $n^4-4n^3+14n^2-20n+10$ is a perfect square, find all integers n that satisfy the condition

Let $f(x)=x^{15}-2017x^{14}+2017x^{13}-2017x^{12}+2017x^{11}-...+2017x^{3}-2017x^{2}+2017x+2017$ What is $f(2016)?$

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

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

Inequality with $a+b+c=1$

If $f : \mathbb R \rightarrow \mathbb R $ such that $f(x^2+x)+2f(x^2-3x+2) = 9x^2-15x$. Find $f(2016)$.

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

Area inside the astroid

Where do I start learning Higher Mathematics?

Negative Modulo confusion

In $\triangle ABC$, find the value of $\tan A\tan C$.

Functional equation $f(a+b)^3-f(a)^3-f(b)^3=3f(a)f(b)f(a+b)$

Solve the equation $p^x-y^p=1$

Prove that one of x,y,z is smaller than 3 and one is bigger than 5 if...

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

Find the value of k when $f(x) = x^3 -4x^2 + 6x + k$

$p^n\mid ((p^{n-m}+1)^j-1)$?

Prove or disprove $\sum\limits_{cyc}\frac{x^4+y^4}{x+y}\le 3\frac{x^4+y^4+z^4}{x+y+z}$

Prove that $a^x \equiv -1 \pmod{p}$ if and only if $k \mid 2x$ but $k \nmid x$

Use mathematical induction to prove that $ \frac{(2n)!}{(2^n)} $ is a natural number for all n $\ge $ 0.

Divisibility of a number of the form $3^{n}-1$

Solving $y+\sqrt{y^2-1}=e^x$ respect to $y$

Directed angles problem: For $A$, $B$, $C$ on $\bigcirc O$, show that $\angle OAC=90^\circ-\angle CBA$

Prove that for all $\alpha + \beta + \gamma = \pi$, $\sum_{cyc}\frac{\sin\beta}{\cos\beta + 1} = \frac{\sum_{cyc}\cos\beta + 3}{\sum_{cyc}\sin\beta}$.

Too many tangents

How to evaluate $\lim_{n \to \infty} \sqrt[n]{\frac{n^3}{2^n + 5^n}}$?