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Daniel Castle

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26 Questions

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votes

answers

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What's really going on behind calculus? [closed]

May 19 '18 at 22:59 B. Mehta 12.1k

votes

answers

552

views

What is known about this sequence?

elementary-number-theory

Nov 27 '17 at 5:34 Daniel Castle 994

votes

answers

517

views

Expression for the highest power of 2 dividing $3^a\left(2b-1\right)-1$

elementary-number-theory prime-factorization collatz

Aug 23 '17 at 15:52 Daniel Castle 994

votes

answer

views

Is it possible to construct modulo classes that cover the integers?

elementary-number-theory elementary-set-theory

Feb 27 at 18:06 Daniel Castle 994

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answers

views

Number of solutions to $x^2+ax=y^2+by$

elementary-number-theory diophantine-equations

Jul 11 '18 at 14:31 Daniel Castle 994

votes

answer

129

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For every $a>4$, $2^{-a-2}\cdot(3^{2^a(2b-1)}-1)$ is odd

number-theory induction

Sep 20 '17 at 17:14 Did 255k

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answers

views

Is this limit for the sum of remainders correct?

limits proof-verification reference-request modular-arithmetic

Aug 6 at 20:07 Thomas Andrews 138k

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answer

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How might I evaluate $\sum_{n=1}^{\infty}\frac{\sin(nx+c)}{n}$?

calculus sequences-and-series trigonometry complex-numbers

Mar 26 at 22:58 Mark Viola 138k

votes

answer

views

Is this formula correct?

sequences-and-series fourier-series

Mar 21 at 4:33 marty cohen 86k

votes

answers

153

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Finding an expression for $\prod_{x=1}^n(1-f(x))$

elementary-number-theory statistics

Nov 23 '17 at 3:06 John Barber 3,044

votes

answers

100

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Highest power of 2 dividing $(3^a-2^a)\cdot(2b-1)-1$?

elementary-number-theory

Sep 20 '17 at 19:25 Daniel Castle 994

votes

answers

109

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Unsure about the relationships created by $LCM(1, 2,…, n)$

prime-numbers least-common-multiple

May 28 '17 at 15:47 Will Jagy 112k

vote

answers

views

Are these results on sums of powers of remainders correct?

limits elementary-number-theory reference-request

Nov 17 at 19:57 Daniel Castle 994

vote

answer

views

Can all even numbers be written in this form?

elementary-number-theory

Nov 5 '17 at 2:32 Robert Soupe 13.3k

vote

answer

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Trying to show if $a=(b+1)c+\frac{1}{2}b(b-1)$ then $a\not=2^d+1$

elementary-number-theory proof-writing divisibility

Nov 1 '17 at 19:36 Aqua 64.1k

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answer

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Mapping numbers in some interval uniquely

elementary-number-theory

Oct 25 '17 at 23:11 RGS 9,347

vote

answer

147

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Trying to understand this Collatz investigation result

elementary-number-theory collatz

Sep 25 '17 at 9:33 Collag3n 1,105

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answers

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How might I find the values of $a$ in terms of $b$ such that ${2^a}+1=3^{b}c$?

elementary-number-theory

Jul 4 '17 at 0:17 Distance 33

vote

answers

views

Ordering pairs of integers $(n, m)$ by the value of ${k_1}^n{k_2}^m$

elementary-number-theory

Mar 2 '17 at 10:22 Dean Young 3,932

vote

answers

views

Sequences of differences between integers with a lowest prime factor of some prime.

prime-numbers prime-gaps

Feb 20 '17 at 23:11 Daniel Castle 994

votes

answer

views

Is this divisor function limit correct?

limits elementary-number-theory

Aug 15 at 18:54 Daniel 2,437

votes

answers

views

Upper bound for the divisor counting function?

elementary-number-theory divisor-counting-function

Jul 11 '18 at 21:53 Daniel Castle 994

votes

answers

views

Finding an expression/approximation of this product

calculus sequences-and-series summation

Nov 28 '17 at 9:08 robjohn♦ 284k

votes

answer

views

Relating the highest powers of 2 in $a$ and $b$ to $a+b$

elementary-number-theory

Sep 20 '17 at 14:02 Arthur 150k

votes

answer

313

views

How would I find a closed form expression of this sum?

summation

Jul 3 '17 at 1:14 Dhruv Kohli - expiTTp1z0 4,817

votes

answer

views

What is the range of integers that only have prime factors of a prime, $p$, or less? [closed]

prime-numbers

Dec 13 '16 at 19:58 Daniel Castle 994

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26 Questions

What's really going on behind calculus? [closed]

What is known about this sequence?

Expression for the highest power of 2 dividing $3^a\left(2b-1\right)-1$

Is it possible to construct modulo classes that cover the integers?

Number of solutions to $x^2+ax=y^2+by$

For every $a>4$, $2^{-a-2}\cdot(3^{2^a(2b-1)}-1)$ is odd

Is this limit for the sum of remainders correct?

How might I evaluate $\sum_{n=1}^{\infty}\frac{\sin(nx+c)}{n}$?

Is this formula correct?

Finding an expression for $\prod_{x=1}^n(1-f(x))$

Highest power of 2 dividing $(3^a-2^a)\cdot(2b-1)-1$?

Unsure about the relationships created by $LCM(1, 2,…, n)$

Are these results on sums of powers of remainders correct?

Can all even numbers be written in this form?

Trying to show if $a=(b+1)c+\frac{1}{2}b(b-1)$ then $a\not=2^d+1$

Mapping numbers in some interval uniquely

Trying to understand this Collatz investigation result

How might I find the values of $a$ in terms of $b$ such that ${2^a}+1=3^{b}c$?

Ordering pairs of integers $(n, m)$ by the value of ${k_1}^n{k_2}^m$

Sequences of differences between integers with a lowest prime factor of some prime.

Is this divisor function limit correct?

Upper bound for the divisor counting function?

Finding an expression/approximation of this product

Relating the highest powers of 2 in $a$ and $b$ to $a+b$

How would I find a closed form expression of this sum?

What is the range of integers that only have prime factors of a prime, $p$, or less? [closed]