# Tagged Questions

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### How do I work out the aspect ratio from the resolution by hand?

For $1024 \times 768$ I can see that $768/1024 = 0.75$, i.e. $\frac34$, so $4:3$ makes sense. How do I do it for other resolutions like $1920 \times 1080$ though?
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Definition: suppose a quantity $P$ is identified by $$\frac{P}{k}\simeq \frac{P}{k}+1$$ what we mean is that $$P= 0\pmod{k}.$$ That means that when $P \to P+k$, then \frac{P}{k}\to ... 1answer 42 views ### The elegant expression in terms of gcd and lcm - algebra Given three positive integer numbers k_1, k_2, k_3, we may denote their greatest common divisor(gcd) by \gcd(k_i,k_j)\equiv k_{ij} for gcd of a two pair of number k_i,k_j. ... 2answers 60 views ### Proper decimal fraction for \frac{4n+1}{n(2n-1)} Assume I have a function f(n) = \frac{4n+1}{n(2n-1)} with n \in \mathbb{N} \setminus \left\{ 0 \right\}. The objective is to find all n for which f(n) has a proper decimal fraction. I know ... 3answers 40 views ### Divisibility in base 7 problem Find all integers between 0 \leq a \leq 2400 such they are divisible by 8 and that their base 7 development has at least 3 equal digits. 2answers 58 views ### Using GCD/GCF to find number of intersections in a grid The question I was trying to solve was: A rectangular floor 24×40 is covered by squares of sides 1. A chalk line is drawn from one corner to the diagonally opposite corner. How many tiles have ... 2answers 101 views ### Prove that 3^{n+1}+3^n+3^{n-1} is divisible by 13. Prove that 3^{n+1}+3^n+3^{n-1} is divisible by 13 for all positive integral values of n. I tried: 3^n \cdot 3^1+3^n+3^n\cdot\frac{1}{3} Then what should I do next? Help please? 2answers 50 views ### True or false division algorithm problem Let a,b,c be integers with a not equal to 0 and (b,c)=1. If a divides the product of bc, then a must divide b or a must divide c. My thoughts: I can prove this if (a,b)=1. but I believe it is false ... 2answers 33 views ### If u|s and v|t and gcd(s,t) = 1 then gcd(u,v) = 1 Proposition 1. If \def\divides\mathrel{|}u \divides s and v \divides t and \gcd(s,t) = 1 then \gcd(u,v) = 1. Solution. Assume u \divides s and v \divides t. Since \gcd(u, v) \divides u, ... 0answers 43 views ### Proof that  k^2<2^k [duplicate] I'm struggling with this problem of proof by induction: For any natural number k\geq 5, prove that k^2<2^k. I assumed that k^2<2^k I want to show that (k+1)^2<2^{k+1} The ... 6answers 124 views ### Proof that n^3-n is a multiple of 3. [duplicate] I'm struggling with this problem of proof by induction: For any natural number n, prove that n^3-n is a multiple of 3. I assumed that k^3-k=3r I want to ... 8answers 268 views ### Why is 2x^3 + x, where x \in \mathbb{N}, always divisible by 3? So, do you guys have any ideas? Sorry if this might seem like dumb question, but I have asked everyone I know and we haven't got a clue. 1answer 60 views ### Solving \frac{{2{x^3} - 11x + 6}}{{x - 2}} using algebraic juggling Answer: \eqalign{ & \frac{{2{x^3} - 11x + 6}}{{x - 2}} = \frac{{2{x^2}(x - 2) + 4{x^2} - 11x + 6}}{{(x - 2)}} \cr & = 2{x^2} + \frac{{4x(x - 2) - 8x + 11x + 6}}{{x - 2}} \cr ... 1answer 29 views ### working out a percentage from my email open rates i have the following numbers: recipients: 95 opens: 39 bounces: 2 how would i get the percentage value per open? accoridng to this post: ... 2answers 140 views ### What is an effective means to make divisibility tests a mathematical 'habit', particularly for algebra? Divisibility tests are a useful problem-solving technique for particularly dealing with larger numbers (thousands etc) and algebraic problems. However, I have always found that many students will just ... 7answers 656 views ### n^5-n is divisible by 10? I was trying to prove this, and I realized that this is essentially a statement that n^5 has the same last digit as n, and to prove this it is sufficient to calculate n^5 for 0-9 and see that ... 1answer 100 views ### Finding Pitch Diameter of sprocket I am currently following a tutorial on Instructables here. In the instructable to find the pitch diameter of a sprocket they use the formula on the above link. the pitch that is used is 12.70, the ... 3answers 176 views ### Proving that \frac{n+1}{2n+3} is irreducible I am trying to solve the following problem: Prove that the following fractions are irreducible for any n (n is a natural number and it cannot be null). \frac{n}{n+1} \frac{n+1}{2n+3} ... 3answers 411 views ### The positive integer solutions for 2^a+3^b=5^c What are the positive integer solutions to the equation2^a + 3^b = 5^c$$Of course (1,\space 1, \space 1) is a solution. 1answer 142 views ### Divide N items into M groups with as near equal size as possible Im trying to split (say) N pink, fluffy balls into M groups as evenly as possible. Eg: ... 4answers 853 views ### If n = m^3 - m for some integer m, then n is a multiple of 6 I am trying to teach myself mathematics (I have no access to a teacher), but I am not getting very far. I am just working through the exercises at the end of the book's chapter, but unfortunately ... 3answers 123 views ### Divide with remainder \frac{x^2}{x^2 + x + 2} I am having a hard time long dividing:$$\frac{x^2}{x^2 + x + 2}. Could someone please show a step by step way to divide this, as I can only get it down to : $1 + \frac{x^2}{x + 2}$. Thank you ...
Solution to problem Hi, I'm correcting my work for study, and I cant get my head around this sum. I understand where the $x^2 + x − cx$ comes from but then when the 6 appears it loses me.
### Prove that $(n-m) \mid (n^r - m^r)$
In respect to a larger proof I need to prove that $(n-m) \mid (n^r - m^r)$ (where $\mid$ means divides, i.e., $a \mid b$ means that $b$ modulus $a$ = $0$). I have played around with this for a while ...