User Clyde Kertzer

8 votes

Prove that $1^k + 2^k + \cdots + n^k$ is divisible by $1 + 2 + \cdots + n$

answered Feb 8, 2023 at 19:57

7 votes

What progress has been made on the Collatz conjecture since Crandall's 1978 paper?

answered Feb 9, 2023 at 5:05

6 votes

Determine at what points the complex function $f\left(z\right)=e^{2x}\cos3x+ie^{3x}\sin2y$ is differentiable.

answered Apr 21, 2022 at 18:34

5 votes

Accepted

Is $\left(\frac{a^2}{5}\right)=1$ for all $a$ not divisible by 5?

answered May 2, 2022 at 2:22

4 votes

What is the difference between residue and remainder?

answered May 4, 2022 at 16:42

4 votes

How do I see if $a^3+b^3=c^3+d^3$ has any solutions where $ 1 \le a,b,c,d \in \mathbb{Z} \le 1000$ and $a \ne b \ne c \ne d$?

answered Feb 16, 2023 at 3:10

4 votes

Complex analysis book recommendations with more exercise than Ahlfors' book.

answered Apr 30 at 17:33

3 votes

Accepted

Is there a field of mathematics that deals with the strange properties of numbers?

answered Feb 24, 2023 at 20:49

3 votes

Accepted

A proof of the theorem $1+\frac{1}{2}+\dots+\frac{1}{n} = \frac{k}{m}$ with $k$ odd and $m$ even

answered Feb 9, 2023 at 5:55

3 votes

Accepted

Where does this identity come from: $\left(x^2+7xy-9y^2\right)^3+\left(2x^2-5xy+12y^2\right)^3=\left(2x^2+10y^2\right)^3+\left(x^2-9xy-y^2\right)^3$

answered Feb 8, 2023 at 2:35

3 votes

Accepted

Proof that Corresponding Angle Postulate $\iff$ Playfair's Postulate

answered Feb 16, 2023 at 23:54

3 votes

Is $y' + 3xy + 2 = 0$ a linear first order differential equation?

answered May 3, 2022 at 2:40

3 votes

Accepted

For $n \geq 6$, why are the number of prime pairs $(p,q)$ where $p+q=6n$ > $6n+2$ and $6n+4$ pairs?

answered Apr 4, 2022 at 15:19

3 votes

Accepted

Proving that a number of the form $a^2+1$ can be represented as a product of primes all of the form $4x+1$ along with possibly 2

answered Apr 17, 2022 at 22:26

2 votes

Accepted

Fastest way to simplify large fractions?

answered Mar 29, 2022 at 17:32

2 votes

Expressing any positive number as a sum of distinct primes.

answered Mar 29, 2022 at 18:31

2 votes

Exponential manipulation: is $8^x-2^x=(8 - 2)^x$ valid?

answered May 3, 2022 at 15:02

2 votes

Only $1$ and $4900$ are squares as $1+4+9+\ldots+ n^2$

answered Feb 8, 2023 at 2:57

2 votes

If $N$ divides $a$ and $N$ divides $b$ then

answered Feb 9, 2023 at 17:51

2 votes

Accepted

Show that $\lim _{n \rightarrow \infty} \frac{1}{4^n} h\left(2^n P\right)$ exists

answered Mar 7, 2023 at 21:55

2 votes

Find $x, y$ are natural numbers such that $x^2+16=5^y$

answered Mar 16, 2023 at 5:28

2 votes

Accepted

Will $-b=\sqrt{a}$ always lead to an extraneous solution?

answered Feb 22, 2023 at 2:26

2 votes

Accepted

Prove that $\lfloor {(\frac{\sqrt{5}+1}{2})}^{4n-2}\rfloor-1$ is a square number where $n$ is a natural number.

answered Feb 9, 2023 at 1:40

2 votes

Accepted

Find the radius of convergence of $\sum_{n=0}^{\infty}{\ln\left(\cos{\frac{1}{3^n}}\right)x^n}$

answered Feb 9, 2023 at 6:12

1 vote

Accepted

Primes congruent to $1$ mod $4$ are sum of two squares

answered Feb 9, 2023 at 5:35

1 vote

Solve $\left\lfloor x - 1/2 \right\rfloor^2 = 25$

answered Feb 16, 2023 at 1:59

1 vote

Modulus operation with respect to a sequence

answered Feb 9, 2023 at 6:19

1 vote

Is this proof of special case of Fermat's last theorem correct?

answered Feb 10, 2023 at 20:46

1 vote

Prove that the number of acceptable sequences of integers is $(n+1)!$

answered Feb 10, 2023 at 6:13

1 vote

Rationalize $\frac{\sqrt{t}}{\sqrt[4]{t}+\sqrt{t}}$

answered Feb 9, 2023 at 5:19

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75 Answers

Prove that $1^k + 2^k + \cdots + n^k$ is divisible by $1 + 2 + \cdots + n$

What progress has been made on the Collatz conjecture since Crandall's 1978 paper?

Determine at what points the complex function $f\left(z\right)=e^{2x}\cos3x+ie^{3x}\sin2y$ is differentiable.

Is $\left(\frac{a^2}{5}\right)=1$ for all $a$ not divisible by 5?

What is the difference between residue and remainder?

How do I see if $a^3+b^3=c^3+d^3$ has any solutions where $ 1 \le a,b,c,d \in \mathbb{Z} \le 1000$ and $a \ne b \ne c \ne d$?

Complex analysis book recommendations with more exercise than Ahlfors' book.

Is there a field of mathematics that deals with the strange properties of numbers?

A proof of the theorem $1+\frac{1}{2}+\dots+\frac{1}{n} = \frac{k}{m}$ with $k$ odd and $m$ even

Where does this identity come from: $\left(x^2+7xy-9y^2\right)^3+\left(2x^2-5xy+12y^2\right)^3=\left(2x^2+10y^2\right)^3+\left(x^2-9xy-y^2\right)^3$

Proof that Corresponding Angle Postulate $\iff$ Playfair's Postulate

Is $y' + 3xy + 2 = 0$ a linear first order differential equation?

For $n \geq 6$, why are the number of prime pairs $(p,q)$ where $p+q=6n$ > $6n+2$ and $6n+4$ pairs?

Proving that a number of the form $a^2+1$ can be represented as a product of primes all of the form $4x+1$ along with possibly 2

Fastest way to simplify large fractions?

Expressing any positive number as a sum of distinct primes.

Exponential manipulation: is $8^x-2^x=(8 - 2)^x$ valid?

Only $1$ and $4900$ are squares as $1+4+9+\ldots+ n^2$

If $N$ divides $a$ and $N$ divides $b$ then

Show that $\lim _{n \rightarrow \infty} \frac{1}{4^n} h\left(2^n P\right)$ exists

Find $x, y$ are natural numbers such that $x^2+16=5^y$

Will $-b=\sqrt{a}$ always lead to an extraneous solution?

Prove that $\lfloor {(\frac{\sqrt{5}+1}{2})}^{4n-2}\rfloor-1$ is a square number where $n$ is a natural number.

Find the radius of convergence of $\sum_{n=0}^{\infty}{\ln\left(\cos{\frac{1}{3^n}}\right)x^n}$

Primes congruent to $1$ mod $4$ are sum of two squares

Solve $\left\lfloor x - 1/2 \right\rfloor^2 = 25$

Modulus operation with respect to a sequence

Is this proof of special case of Fermat's last theorem correct?

Prove that the number of acceptable sequences of integers is $(n+1)!$

Rationalize $\frac{\sqrt{t}}{\sqrt[4]{t}+\sqrt{t}}$