Stack Exchange

anonymous

New York, United States

top accounts reputation activity subscriptions
Top Questions
16 votes

Variation on Pythagoras: If $a^2 + b^2 = c^2$, then $a + b \leq c\sqrt{2}$

calculus algebra-precalculus trigonometry inequality proof-strategy asked Jun 19, 2015 at 7:58
math.stackexchange.com

11 votes

Find all strictly increasing functions on positive integers such that $f(f(n))=n+2$

induction functional-equations integers asked Aug 13, 2017 at 10:28
math.stackexchange.com

8 votes

Solve $\sin(5\theta)=1$, $0<\theta<2\pi$. Show that the roots of $16x^4+16x^3-4x^2-4x+1=0$ are $x=\sin{\frac{(4r+1)\pi}{10}}$, $r=0,2,3,4$.

trigonometry polynomials complex-numbers roots quartic-equations asked Jun 4, 2017 at 23:23
math.stackexchange.com

7 votes

Let $ABC$ be a triangle. Points $D$ and $E$ are located on side $BC$ such that $\angle BAD=\angle DAE=\angle EAC.$ Prove that $AB=AC$.

geometry euclidean-geometry circle asked Jun 29, 2017 at 0:47
math.stackexchange.com

7 votes

Show that, for any two integers $a$ and $b$, at least one of the expressions $a^3, b^3, a^3+b^3$ or $a^3-b^3$ will be divisible by $7$.

number-theory elementary-number-theory proof-verification modular-arithmetic totient-function asked Aug 26, 2017 at 6:51
math.stackexchange.com

5 votes

Find all functions for $x+f(\frac1x) = 2f(x)$

functions functional-equations asked Aug 13, 2017 at 20:43
math.stackexchange.com

5 votes

Laying cable across a river

algebra-precalculus word-problem asked Jun 18, 2015 at 7:24
math.stackexchange.com

5 votes

Find all functions of the form $f(x)=\frac{b}{cx+1}$ where $f(f(f(x)))=x .$

elementary-number-theory functions polynomials asked Jun 24, 2017 at 7:49
math.stackexchange.com

5 votes

Is Keno a fair game?

probability probability-theory soft-question gambling asked Jun 24, 2015 at 20:19
math.stackexchange.com

5 votes

Students in a class, girls sitting with boys and boys sitting with girls

combinatorics elementary-number-theory problem-solving combinations word-problem asked Jun 30, 2015 at 4:16
math.stackexchange.com

1 2

Top Answers