User gandalf61

33 votes

Accepted

Is it possible to shorten the solution for this 2014 RMO question?

answered May 14, 2018 at 11:02

21 votes

Accepted

What is the probability that the first head will appear on the even numbered tosses

probability probability-theory

answered Nov 17, 2017 at 12:12

16 votes

Accepted

Need Help : Proving polynomials are continuous, without circular reasoning

real-analysis limits continuity epsilon-delta

answered Jan 7, 2019 at 9:14

15 votes

Find $\prod^\infty_{n=1} (1 - 10^{-3* 2^n})$.

infinite-product

answered Mar 31, 2017 at 9:02

14 votes

Accepted

Is there a name for categories whose objects are sets?

category-theory terminology

answered Sep 5, 2019 at 19:39

11 votes

Degree of the eighth vertex given the other degrees

graph-theory

answered Apr 30, 2018 at 10:17

11 votes

A quick way, say in a minute, to deduce whether $1037$ is a prime number

algebra-precalculus elementary-number-theory primality-test

answered May 21, 2018 at 9:13

10 votes

Say $a=b$. Is "Do the same thing to both sides of an equation, and it still holds" an axiom?

logic

answered Jun 5, 2018 at 11:34

10 votes

Accepted

Can the inverse of this function be expressed in closed form?

inverse-function

answered Jun 27, 2018 at 10:21

10 votes

Accepted

After deleting the multiples of $2$ and multiples of $3$ from list of integers from $1$ to $N$, why are a fifth of the numbers still multiples of 5?

combinatorics elementary-number-theory prime-numbers

answered Jul 11, 2018 at 10:24

10 votes

How is the similarity of the structure of two functions defined?

functions

answered Apr 12, 2018 at 10:57

10 votes

What are the possible values of these letters?

algebra-precalculus

answered Nov 14, 2018 at 15:26

9 votes

What is the difference between complex numbers and 2D vectors?

vectors geometry complex-numbers

answered Nov 8, 2019 at 11:25

9 votes

Where are the imaginary numbers in Fourier analysis hiding?

fourier-transform complex-numbers

answered Jul 26, 2021 at 11:01

9 votes

Accepted

Question on speed.

algebra-precalculus

answered Apr 26, 2018 at 13:38

9 votes

Why is it important for a matrix to be square?

linear-algebra matrices

answered Jun 8, 2018 at 11:55

8 votes

Accepted

What does it mean for something to be a model of hyperbolic space?

hyperbolic-geometry curvature

answered Jul 17, 2018 at 11:44

8 votes

Accepted

Find the limit of sequence $\frac{1}{2}+\frac{3}{2^{2}}+\frac{5}{2^{3}}+\cdots+\frac{2n-1}{2^{n}}$ without using of derivatives and etc.

sequences-and-series limits

answered Apr 11, 2018 at 11:53

8 votes

How would antique math books compare to modern books?

math-history

answered Apr 13, 2017 at 11:27

8 votes

Can we say that an element is not a subset of a set?

elementary-set-theory

answered Apr 20, 2017 at 9:53

8 votes

Limit of a sequence of integrals involving continued fractions

calculus limits definite-integrals continued-fractions

answered Nov 19, 2018 at 10:51

7 votes

Unexplained log simplification, can someone show how?

logarithms

answered Oct 10, 2020 at 20:38

7 votes

Number of positive real roots in equation $x^6 - x - 1 =0$

real-analysis

answered May 4, 2018 at 10:34

7 votes

How is $0$ generated from $1$ or $-1$?

group-theory

answered Dec 26, 2017 at 4:44

7 votes

Let k be an integer. Disprove: “The equation $x^2 − x − k = 0$ has no integer solution if and only if $k$ is odd.”

elementary-number-theory proof-verification diophantine-equations quadratics

answered Jan 23, 2019 at 10:29

6 votes

Without using a calculator can you say, which number is greater, $65^{1662}$ or $33^{1995}$?

discrete-mathematics exponential-function

answered Jan 8, 2020 at 9:40

6 votes

What's the intuition behind the fact that you can factorise an expression as $(x-a)(x-b)$ if $a$ and $b$ are the roots of the expression

functions roots

answered Jul 25, 2018 at 13:23

6 votes

Prove all derivatives of $f(x)=\frac{1}{1+x}$ by induction

real-analysis derivatives induction

answered Oct 4, 2018 at 16:40

5 votes

Accepted

Calculate the value of $\frac{1}{2}+\frac{1}{4}+\frac{2}{8}+\frac{3}{16}+....+\frac{F_n}{2^n}+....$

sequences-and-series number-theory contest-math fibonacci-numbers

answered Oct 3, 2019 at 11:17

5 votes

What is the number of pairs of $(a,b)$ of positive real numbers satisfying $a^4+b^4<1$ and $a^2+b^2>1$?

combinatorics inequality triangles real-numbers

answered Feb 22, 2019 at 14:41

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688 Answers

Is it possible to shorten the solution for this 2014 RMO question?

What is the probability that the first head will appear on the even numbered tosses

Need Help : Proving polynomials are continuous, without circular reasoning

Find $\prod^\infty_{n=1} (1 - 10^{-3* 2^n})$.

Is there a name for categories whose objects are sets?

Degree of the eighth vertex given the other degrees

A quick way, say in a minute, to deduce whether $1037$ is a prime number

Say $a=b$. Is "Do the same thing to both sides of an equation, and it still holds" an axiom?

Can the inverse of this function be expressed in closed form?

After deleting the multiples of $2$ and multiples of $3$ from list of integers from $1$ to $N$, why are a fifth of the numbers still multiples of 5?

How is the similarity of the structure of two functions defined?

What are the possible values of these letters?

What is the difference between complex numbers and 2D vectors?

Where are the imaginary numbers in Fourier analysis hiding?

Question on speed.

Why is it important for a matrix to be square?

What does it mean for something to be a model of hyperbolic space?

Find the limit of sequence $\frac{1}{2}+\frac{3}{2^{2}}+\frac{5}{2^{3}}+\cdots+\frac{2n-1}{2^{n}}$ without using of derivatives and etc.

How would antique math books compare to modern books?

Can we say that an element is not a subset of a set?

Limit of a sequence of integrals involving continued fractions

Unexplained log simplification, can someone show how?

Number of positive real roots in equation $x^6 - x - 1 =0$

How is $0$ generated from $1$ or $-1$?

Let k be an integer. Disprove: “The equation $x^2 − x − k = 0$ has no integer solution if and only if $k$ is odd.”

Without using a calculator can you say, which number is greater, $65^{1662}$ or $33^{1995}$?

What's the intuition behind the fact that you can factorise an expression as $(x-a)(x-b)$ if $a$ and $b$ are the roots of the expression

Prove all derivatives of $f(x)=\frac{1}{1+x}$ by induction

Calculate the value of $\frac{1}{2}+\frac{1}{4}+\frac{2}{8}+\frac{3}{16}+....+\frac{F_n}{2^n}+....$

What is the number of pairs of $(a,b)$ of positive real numbers satisfying $a^4+b^4<1$ and $a^2+b^2>1$?