User Oscar Lanzi

67 votes

Is the "determinant" that shows up accidental?

answered Mar 25, 2018 at 11:32

63 votes

Are rational points dense on every circle in the coordinate plane?

general-topology coordinate-systems rational-numbers

answered Oct 23, 2018 at 2:15

37 votes

Accepted

Alternating series; first term is 0. Do I have a problem?

real-analysis sequences-and-series

answered Dec 31, 2016 at 0:44

35 votes

Is the arc length always irrational between two rational points?

calculus irrational-numbers pi arc-length

answered Jul 11, 2019 at 9:57

33 votes

Multiple-choice: sum of primes below $1000$

algebra-precalculus summation

answered Jan 30, 2017 at 2:01

30 votes

Accepted

Why does the circle intersect the line?

geometry euclidean-geometry

answered Jun 3, 2018 at 20:09

26 votes

What problems have been frequently computationally verified for large values?

reference-request recreational-mathematics math-history big-list

answered Aug 6, 2018 at 20:57

25 votes

Best approximation of log 3?

calculus logarithms

answered Aug 22, 2017 at 10:22

21 votes

Accepted

How to solve this solvable 8th-degree algebraic equation by radicals?

abstract-algebra polynomials gap

answered Jan 25 at 17:54

20 votes

Accepted

Is there an easy way to see that ${1\over5} + \frac{1}{6} + \frac{1}{7} + \frac{1}{8} + \frac{1}{9} + \frac{1}{10} + \frac{1}{11} + \frac{1}{12} > 1$?

inequality fractions cauchy-schwarz-inequality harmonic-numbers number-comparison

answered Jan 19, 2020 at 0:08

17 votes

Accepted

An algebraic riddle: The king's chest full of bags of gold coins

inequality

answered Aug 18, 2017 at 10:15

16 votes

Is there a surface on which a hexagon can have all right angles?

geometry

answered Nov 30, 2018 at 2:59

14 votes

Accepted

Is there a proof that doubling the sum of squares of any two integers will always equate to another sum of two squares?

integers

answered Jan 10, 2020 at 2:22

14 votes

Unexpected examples of natural logarithm

soft-question logarithms big-list

answered Jul 3, 2017 at 15:35

14 votes

Is the catenary the trajectory of anything?

calculus

answered Apr 7, 2016 at 2:12

13 votes

Accepted

$\tan(z)=i$, no solution

proof-verification complex-numbers

answered Jul 9, 2018 at 20:18

12 votes

Prove that $23$ does not divide $2^n + 3^m$, for any $m, n \in \mathbb{N}$

number-theory modular-arithmetic

answered Feb 3, 2017 at 11:46

12 votes

How can a mug and a torus be equivalent if the mug is chiral?

general-topology geometric-topology

answered Apr 30, 2017 at 0:37

11 votes

Why doesn't $\int\lfloor {x}\rfloor~dx=x\lfloor x\rfloor +C$?

calculus integration indefinite-integrals ceiling-and-floor-functions fake-proofs

answered Jun 28, 2021 at 13:06

11 votes

Help with $\int _0^{\infty }\frac{\sinh \left(x\right)}{x\cosh ^2\left(x\right)}\:\mathrm{d}x$

calculus integration definite-integrals

answered Jul 15, 2021 at 17:33

11 votes

Accepted

Showing that $4b^2+4b = a^2+a$ has no non-zero integer solutions?

algebra-precalculus elementary-number-theory

answered Jun 25, 2018 at 14:32

10 votes

Why is the "solving for cubic equation roots general rule" sometimes not applicable while the equation obviously has roots?

linear-algebra functions roots

answered Mar 7, 2020 at 15:25

10 votes

Prove the following trigonometric identity without a calculator involved

trigonometry

answered Feb 17, 2016 at 17:21

9 votes

Happy $\pi$-day! Is it true that $\sum_{p \;\text{prime} } \frac{1}{{\pi}^p} < \pi -\lfloor \pi \rfloor$?

real-analysis calculus sequences-and-series approximation pi

answered Mar 14, 2020 at 2:17

9 votes

$6!\cdot 7!=10!$. Is there a natural bijection between $S_6\times S_7$ and $S_{10}$?

combinatorics

answered Nov 21, 2020 at 13:20

9 votes

Accepted

prove that $X^2 \equiv 35 \pmod{100}$ has no solutions

elementary-number-theory proof-verification

answered Sep 23, 2018 at 17:47

9 votes

How to solve the differential equation $xx'' = (x')^2$?

ordinary-differential-equations

answered May 11, 2018 at 9:56

8 votes

A possible solution to $\sqrt {5-x}=5-x^2$ (without taking square from both sides)

algebra-precalculus polynomials solution-verification radicals functional-equations

answered Apr 6, 2020 at 20:30

8 votes

Accepted

Simple continued fraction of $\sqrt{d}$ with period of shortest length $3$

elementary-number-theory continued-fractions

answered Nov 9, 2019 at 15:07

8 votes

Accepted

What is the smallest possible value of $q$ such that $\frac{7}{10}<\frac{p}{q}<\frac{11}{15}$?

algebra-precalculus

answered Sep 11, 2019 at 15:11

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1,153 Answers

Is the "determinant" that shows up accidental?

Are rational points dense on every circle in the coordinate plane?

Alternating series; first term is 0. Do I have a problem?

Is the arc length always irrational between two rational points?

Multiple-choice: sum of primes below $1000$

Why does the circle intersect the line?

What problems have been frequently computationally verified for large values?

Best approximation of log 3?

How to solve this solvable 8th-degree algebraic equation by radicals?

Is there an easy way to see that ${1\over5} + \frac{1}{6} + \frac{1}{7} + \frac{1}{8} + \frac{1}{9} + \frac{1}{10} + \frac{1}{11} + \frac{1}{12} > 1$?

An algebraic riddle: The king's chest full of bags of gold coins

Is there a surface on which a hexagon can have all right angles?

Is there a proof that doubling the sum of squares of any two integers will always equate to another sum of two squares?

Unexpected examples of natural logarithm

Is the catenary the trajectory of anything?

$\tan(z)=i$, no solution

Prove that $23$ does not divide $2^n + 3^m$, for any $m, n \in \mathbb{N}$

How can a mug and a torus be equivalent if the mug is chiral?

Why doesn't $\int\lfloor {x}\rfloor~dx=x\lfloor x\rfloor +C$?

Help with $\int _0^{\infty }\frac{\sinh \left(x\right)}{x\cosh ^2\left(x\right)}\:\mathrm{d}x$

Showing that $4b^2+4b = a^2+a$ has no non-zero integer solutions?

Why is the "solving for cubic equation roots general rule" sometimes not applicable while the equation obviously has roots?

Prove the following trigonometric identity without a calculator involved

Happy $\pi$-day! Is it true that $\sum_{p \;\text{prime} } \frac{1}{{\pi}^p} < \pi -\lfloor \pi \rfloor$?

$6!\cdot 7!=10!$. Is there a natural bijection between $S_6\times S_7$ and $S_{10}$?

prove that $X^2 \equiv 35 \pmod{100}$ has no solutions

How to solve the differential equation $xx'' = (x')^2$?

A possible solution to $\sqrt {5-x}=5-x^2$ (without taking square from both sides)

Simple continued fraction of $\sqrt{d}$ with period of shortest length $3$

What is the smallest possible value of $q$ such that $\frac{7}{10}<\frac{p}{q}<\frac{11}{15}$?