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Clyde Kertzer's user avatar
Clyde Kertzer's user avatar
Clyde Kertzer's user avatar
Clyde Kertzer
  • Member for 2 years, 5 months
  • Last seen this week
8 votes

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

7 votes

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

6 votes

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

5 votes
Accepted

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

5 votes

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

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 $a \ne b \ne c \ne d$?

4 votes

What is the difference between residue and remainder?

3 votes
Accepted

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

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

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?

3 votes

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

3 votes
Accepted

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

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

3 votes
Accepted

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

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.

2 votes
Accepted

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

2 votes
Accepted

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

2 votes
Accepted

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

2 votes

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

2 votes
Accepted

Fastest way to simplify large fractions?

2 votes

Expressing any positive number as a sum of distinct primes.

2 votes

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

2 votes

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

2 votes

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

1 vote

Find the smallest number which leaves remainder 1, 2 and 3 when divided by 11, 51 and 91

1 vote

What is the method to solve this kind of problems in modular arithmetic?

1 vote
Accepted

Find integers $0 < v < u$ that are coprime, yet the Pythagorean triple $(u^2-v^2, 2uv, v^2 + u^2)$ is not primitive

1 vote

Inverse of $ 3\cdot\frac 57 \mod 7 $

1 vote

What is the line of thinking to get $[(n^2+3n+1)^2-5n(n+1)^2]$ from $(n^4+n^3+n^2+n+1)$?

1 vote

Products of primes up to the $n$th prime