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Oct
26
answered How can I show that $n! \leqslant (\frac{n+1}{2})^n$?
Oct
26
answered Are conditions equaivalent that they are roots of unity?
Oct
26
comment Help with a hyperbolic trig problem
@user183782, Solve for $a=e^n$ and then for $n$
Oct
26
comment Help with a hyperbolic trig problem
@user183782, $$a+\frac1a=\pm\sqrt5+1$$ But for real $n,a=e^n>0\implies a+\frac1a\ge2$ $$\implies a+\frac1a=\sqrt5+1$$ Solve for $a$. But, what is $x?$
Oct
26
revised Help with a hyperbolic trig problem
edited body
Oct
26
comment If $a+\frac1a=\sqrt3$ then $a^4+\frac1{a^4}=\ ?$
@Nick, Thanks for your feedback. What about my other answer?
Oct
26
comment Proof for $\gcd(F_m,F_n)=F_{\gcd(n,m)}$
math.hmc.edu/funfacts/ffiles/20004.5.shtml
Oct
26
comment Help with a hyperbolic trig problem
@Dr.SonnhardGraubner, Thanks for your observation
Oct
26
revised Help with a hyperbolic trig problem
edited body
Oct
26
comment Find all $x \in\mathbb Z$ such that $16x\equiv 26\pmod{42}$
@MiloszWielondek, The answer of the last question is "Yes". $$16x\equiv26\pmod{42}\iff16x=26+42z\iff8x=13+21z$$ where $z$ is some integer
Oct
26
answered Help with a hyperbolic trig problem
Oct
26
comment Find the area of triangle APB, where P is a point $(a\cos\theta, b\sin\theta)$ on an ellipse and $A, B$ are its radii points $(a,0) (0,b)$
Use mathopenref.com/coordtrianglearea.html or math.stackexchange.com/questions/516219/…
Oct
26
answered If $a+\frac1a=\sqrt3$ then $a^4+\frac1{a^4}=\ ?$
Oct
26
answered If $a+\frac1a=\sqrt3$ then $a^4+\frac1{a^4}=\ ?$
Oct
26
answered Find all $x \in\mathbb Z$ such that $16x\equiv 26\pmod{42}$
Oct
26
comment Prove or disprive that $n^{2}-n+17$ is prime for all integers $n$
See mathworld.wolfram.com/Prime-GeneratingPolynomial.html and en.wikipedia.org/wiki/Formula_for_primes
Oct
26
comment Discrete algebra and exponents (See body text)
@CoinToss, $$a^{\phi(m)}\equiv1\pmod m\implies (a^{\phi(m)})^r\equiv1^r\equiv1$$ right?
Oct
26
comment Prove this equality
Let $$\sqrt[3]{2+11i}+\sqrt[3]{2-11i}=y$$ $$y^3=2+11i+2-11i+3\sqrt[3]{(2+11i)(2-11i)}y=4+15y$$
Oct
26
answered Find $a^2 + b^2+c^2$
Oct
22
comment The residue of $x^{15}-1$ divided by $x^2-1$
$$x((x^2)^7-1^7)+x-1$$ Now use math.stackexchange.com/questions/188657/…