Questions on basic arithmetic involving numerical quantities only. Questions involving variable values (other than the result of the operation) should be placed under the (algebra-precalculus) tag.

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Pos properties.

Given $n\in\mathbb{N}$, and $f:\mathbb{N}^*\rightarrow \mathbb{N}$, let define $Pos$ as: $$Pos(f)(n)= |\{x \leq n, f(x)=f(n)\}|$$ When given $n\in\mathbb{N}$, this function gives the 'position' of $...
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2answers
26 views

Number patterns of fractions

I can't seem to find a difference for this number pattern .. Given a sequence ... $1, 2/3 , 4/7 , 8/15 , 16/31 ... $ What is the next term of the sequence ? I can't seem to spot a difference ...
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3answers
376 views

Prime numbers on a non-standard model

I can't imagine how this is possible: Let $\mathcal{M}$ be a nonstandard model of arithmetic. Show that: There is an element $a\in M$ such that for all prime numbers $p$, we have that $\mathcal{M} \...
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2answers
38 views

Prove that : $10^{5n+2}+(-1)^{n}\cdot 4 \equiv 0 \pmod {13}$

Prove that : $$10^{5n+2}+(-1)^{n}\cdot 4 \equiv 0 \pmod {13}$$ I don't have enough skills in modular to do it Please help
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0answers
27 views

What is the logic of priority of operations?

For example $2+2\times2$ is $6$ not $8$. Actually $+$ and $\times$ are binary operations on $\mathbb Z$. but here there is an triple $(2,2,2)$ which we sent to $2+2\times 2$. So we have to put and ...
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1answer
42 views

Mathematics- Time and work

A & B can complete a job in 8 days and B & C can do it in 12 days. A & B commence the work and do it for 4 days, then A leaves. B continues for 2 days and leave. C starts working and ...
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1answer
138 views

What is the definition of $n\cdot n\cdot n$?

Intuitively, What does it mean when you multiply numbers? I asked my professor about what does it mean when we multiply $5\cdot 5\cdot 5$. He said there is no definition of this thing in mathematics. ...
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22 views

Characterization of elementary arithmetic operators to explain certain properties in programming languages

In the LISP-like family of programming languages, the four elementary arithmetic operators behave differently: + and * can take ...
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5answers
89 views

How do I average two numbers that are already averaged?

$50$ juniors and seniors are tested. $35$ of them average $80%$. $15$ of them average $70%$. What is the average of the class of $50$? We tried $(70+80)/2$ but that was $75$ and the real answer is ...
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4answers
96 views

Easier way to divide a fraction by a fraction.

Say this is the problem: $$\frac{3/8}{4/5}$$ As of right now, I would multiply both fractions by $40$ then simplify to get $\frac{15}{32}$ Or I would multiply $\frac{3}{8}$ and $\frac{5}{4}$ to ...
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0answers
38 views

Need a hint to solve example…

I can solve this type of problem first time so need hint what can I do and where I get such more problem. The Value of $$100\left[\frac{1}{(1)(2)}+\frac{1}{(2)(3)}+ \frac{1}{(3)(4)}+\ldots+\frac{1}{(...
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1answer
43 views

General formula for the numerators?

Suppose that $a$ is a natural number. The numerator of $\dfrac {1}{a}$ is $1$. The numerator of $\dfrac {1}{a} + \dfrac {1}{a+1}$ is $2a+1$ [Note: Here for our purpose we don't cancel common factors ...
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1answer
44 views

Making a “larger than” function with only basic arithmetic

Is it possible to make a function using only arithmetic (no logic operators), that can return 1 if it's input x is larger than a given number a, and 0 if it's less than a? If it is, how would one ...
4
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1answer
33 views

additive integral property

There's a common property of definite integrals: $\int_a^bf(x) \, dx=\int_a^cf(x)\,dx+\int_c^bf(x)\,dx$. I've often seen it said that $c$ must lie in the interval $[a,b]$. However, is this really the ...
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1answer
32 views

what is the initial temperature of the object? [closed]

I have a question and I cant solve it . I'll be thankful if you solve it for me and give your complete solution. We put an object in a freezer which have -17 degrees temperature. After a few minutes ...
2
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1answer
29 views

Best method to add and subtract (Common Core-ish)

What's the best method for adding and subtracting? I have a son in the third grade so as a parent I'm smack dab in the middle of the common core debate (I'm hoping to avoid the Facebook ...
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2answers
27 views

Fractions (Dividing… Maybe?)

The question... (With mixed fractions) (3)3/4 is bigger than (1)19/21 How many times bigger? I assume you divide the first fraction by the second but I cant seem to do it, could someone maybe answer ...
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2answers
48 views

Definability of the $<$ order relation on the natural numbers using addition. [closed]

Show that the usual order relation $<$ on the natural numbers is definable in the structure $(\mathbb{N}, +)$ with only addition. My teacher has clarified this for me and quantifiers can be used. ...
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2answers
16 views

Calculating a function given a certain x range.

I have the function $f(x) = x^3 + 1$ and I want to calculate the following: $f(x) = (\frac{a}{25})^3 + 1 $ Where "$a$" is 1,2,3,4,..,50. 1 through 50 Basically I'm adding up $f(1) + f(2) + f(3) + ...
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0answers
45 views

Serre mass formula under extension

Suppose $K_1$ is a local field and $K_2$ is a totally ramified finite Galois extension. Let $e$ be a positive integer with $[K_2:K_1]|e$. Consider the set of isomorphism classes of $K_1$ extensions of ...
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1answer
3k views

What is this type of math notation called? (+ 4 5)

So I've been looking for a general name of this type of mathematics notation (google hasn't been very useful) so that I can learn more about it. Basically, the symbols are in the form of functions and ...
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1answer
19 views

(Straight line) Gradient for (-4, 0) (0, 2.5)

So I changed the question the textbook gave me to (-4,0) (0, 5/2). The question asked me what is the gradient for the X and Y.I was doing the question without a calculator and the answer I got was 8/...
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1answer
52 views

Simple Addition Question [closed]

In basic math, when adding there is the notion of carry. For example if you have $9999+9999$, since $9+9=18$ the $1$ is leftover and carried to the top. Is there some formula that gives us the total ...
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1answer
60 views

Inequalities - AM-GM

Let $H_n = 1 + 1/2 + 1/3 + ... + 1/n$ Prove that; $H_n + n$ $\geq$ n$(n+1)^\frac{1}{n}$ for $n$ $\leq$ $2$ I have tried writing $H_n + n = 1/2 + 1/3 +...+ 1/n + (n+1)$ but am left with an $n!$ in ...
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0answers
26 views

If $1/2 ≤ p/q ≤ 2$ , then $p-q$ is representable exactly on the computer

I've found the following affirmation in an article. I've been thinking about it but I don't know the way to prove it: It is not hard to prove that if $p$ and $q$ are two of a computer’s floating–...
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0answers
67 views

How do hyperoperations like tetration exist if operations are seperate relations and not repeatitions of each other.

I've run into a bit of a conflict in my fundamental understanding of concepts in math. I've always known the arithmetic operation to be extensions of each other. Multiplication is repeated addition, ...
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0answers
30 views

Decrementing one number, incrementing another, while keeping the same relation to one another

This is a game development question related to math. Apologies if I shouldn't be asking this here, but I'm not good at math and need help with increasing the speed of my game. I have one number ...
5
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4answers
486 views

A simple binomial identity

Is there a simple way of showing that a prime $p$ must divide the binomial coefficient $p^n\choose{k}$ for all $n\geq 1$ and $1\leq k\leq p^n-1$?
2
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3answers
32 views

Algebra and brackets opening

I'm trying to clarify, how to open brackets. Simple example: $$2a - {4 - [3b -(5a -7 + b)] + 2} = 2a - {4 - 3b +5a +7 - b + 2}$$ As you can see, need to change sign. Opened $()$ changed $-$ to $+$ ...
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2answers
80 views

Finding the general formula of a sequence alternating between even and odd

So I know how to find the general formula of a simple sequence and sequences involving alternating signs but how would you devise a general formula for sequqences alternating between even and odd ...
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4answers
42 views

Explain equality $F(n)=2^{n-1} \cdot 1 \cdot 3 \dots(2n-3)=\frac{(2n-2)!}{(n-1)!}$

$F(n)=2^{n-1} \cdot 1 \cdot 3 \dots(2n-3)=\frac{(2n-2)!}{(n-1)!}$ Any thouts how to prove this equality? Thanks
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0answers
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Is there any equation to find the number of additions in Multiplication?

By seeing this answer that tells "it takes 200 additions for multiplying two 100 digit numbers" I would like to know whether there is any equation to find the number of additions in multiplication.
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0answers
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Method of Complements in Base 17 Given a base 10 number.

Given the following table which shows the symbols I am using when representing numbers in base 17. \begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline 0_{10} & 1_{10} & 2_{10} & ...
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2answers
34 views

Order of precedence, multiplication vs. division

Recently I had this doubt about the order of precedence of mathematical operations multiplication and division. Given that we have a simple question like this ...
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1answer
57 views

Fill in operators (7 7 7 7 7 7 7 7 = 820)

My kid's git the following as his homework - the problem is to fill in arithmetic operators between eight digits 7 to get 820, that is: 7_7_7_7_7_7_7_7=820 This drives me mad, but I myself cannot ...
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3answers
104 views

Mental $n-$th root of $N$

It has been a while since I started thinking about this problem: a fast method to evaluate (in an approximate way) mentally the $n-$th root of a number $N$. I'm talking about great numbers, because ...
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2answers
30 views

Simple existence proofs without bounds

Which is/are the most simple proof/s of an existential statement like $$ \exists x P(x) $$ or $$ \forall x \exists y P(x,y) $$ where the variables rage over the integers, such that the proof doesn't ...
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1answer
36 views

How to square a two digit number without a calculator? [closed]

I will put the answer as an answer as if I post it here then the answer section will be pointless also you can answer your own question so why not?
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2answers
28 views

algorithum math problem

if x, y and z each represent a different digit from 0 to 9, what is the value of (x)(y)(z)? 4z 27 +x5 ____ y14 I answered it like this: ...
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1answer
15 views

Proportion questions relating with 3 subjects .

Eight men can build two houses in 20 days. How man men does it take to build 3 houses in 15 days My workings : $2 houses = 20 days$ $3 houses = 20.2.3= 120 days$ $1 men = 2 houses = 1/20 days$ ...
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1answer
43 views

Three-Terms Ratios.

. How to write these ratios $X:Y:Z$ in terms of fraction i.e. either like $$\frac{\frac{X}{Y}}{Z}$$ or $$\frac{X}{\frac{Y}{Z}}$$?
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2answers
56 views

Simplifying Fractions involving negative numbers

I want to simplify $$\frac{\frac{7}{-10} \times \frac{-15}{6}}{\frac{7}{-19} + \frac{-17}{-8}}$$ I really don't understand how to do this, or even how to start? Negative numbers make it even harder ...
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3answers
35 views

Find a fraction of a part that is shaded

In the figure , O is the centre of the two circles . The circles are divided into sectors of equal sizes. Given that the area of the shaded portion A is twice of the area of the shaded portion B ...
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2answers
48 views

Is there a way to encode all decimal numbers between 0 and 1 into whole numbers?

Is there a way to encode ALL decimal numbers between 0 and 1 into whole numbers with a rationale that supports sum operations between the encoded numbers? so 1=0.1 2=0.2 3=0.3... 1+2 = 3 .. 0.2+0.1 =...
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2answers
43 views

Work and time problem

I came up with this problem: $150$ workers were employed to do a particular work. On first day, $150$ workers worked. On second day, $146$.. and each subsequent day, workers kept on decreasing by 4. ...
2
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4answers
49 views

Numerical property $P(n)$ such that $\forall n P(n)$ is false but a counterexample is difficult to find

I would like to find a nontrivial property $P(n)$ for $n \in \mathbb N$ such that $\forall n P(n)$ is false but the first counterexample can be found only for "very high" $n$ (so high that it wouldn't ...
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0answers
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How can we prove that a number is a prime with some limits? [duplicate]

A simple python program implemented a simple fact that the number is prime if no numbers within it's square root including the square root and excluding 1 divide it. Empirically analyzing it for some ...
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1answer
30 views

multiplying parentheses with more variables than (a b) * (c d)

I want to solve $$ (1 - 2\lambda + \lambda^2)(1 - \lambda) + 2 - 3(1 - \lambda) = 0 $$ Eventually I would probably want to factor the polynomial, but I don't know how to multiply the parentheses of ...
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2answers
32 views

Expansion and factorisation

I have a little problems with a few questions here and I need help.. Thanks ... Factorise completely $$9x^4 - 4x^2 - 9x^2y^2 + 4y^2 $$ My workings .. $$ (3x^2+2x)(3x^2-2x) - y^2 (9x^2-4) = (3x^...
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1answer
18 views

Evaluate by algebraic expansion of factorisation

Evaluate the following by algebraic expansion of factorisation . a) $2007^2$ b) $(503)(497)$ c) $20.5^2 - 19.5^2$ I'm not sure what does it mean by "algebraic expansion of factorisation ." Can I ...