### Questions (220)

 15 If two integer triples have the same sum of 6th powers, then their sums of squares agree $\bmod 9$ 12 Finding Maximum Area of a Rectangle in an Ellipse [duplicate] 8 Separable Differential Equation (Check Answer) 7 Given $x_1 := \sqrt{2}$ and $x_{n+1} :=\sqrt{2x_n}$, prove $\sqrt{2} ≤ x_n ≤ 2$ 7 Find all prime numbers $p$ such that $16p+1$ is a perfect cube

### Reputation (3,223)

 +5 Solve $z^4 = 1$ for all $z$ , Hence or otherwise, solve $z^4 =(z-1)^4$ +5 How would Pythagorean's theorem work in higher dimensions? (General Question) +5 Angle between equal sides of isosceles triangle +5 Consider $I_n=\int^{\frac{\pi}{2}}_0 \frac{\sin(2nx)}{\sin(x)}dx$ , Show that $I_n - I_{n-1}=\frac{2(-1)^{n-1}}{2n-1}$

### Answers (58)

 9 Prove that the root is a whole number 5 Using de Moivre's Theorem to derive formula 5 Prove the Identity $\dfrac{\tan\theta}{\cos\theta-\sec\theta} = -\csc\theta$ 3 Find the locus of $\frac{\pi}{3}\le \arg(-z+3+i)\le \frac{5\pi}{3}$ 3 Convert rectangular equation $(x^2+y^2)^2 - 4(x^2-y^2) = 0$ to polar form

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 19 algebra-precalculus × 37 9 elementary-number-theory × 5 19 calculus × 30 6 derivatives × 19 16 complex-numbers × 38 4 inequality × 12 15 trigonometry × 33 4 geometry × 9 9 linear-algebra × 15 3 integration × 48

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