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Questions tagged [arithmetic]

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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11 views

Floating-point arithmetic M(10,6,6)

Consider arithmetic $M(10,6,6)$, (decimal system, 6 places for mantissa, 6 places for exponent). I have to find the largest positive and smallest positive number in this arithmetic. I was looking ...
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4answers
43 views

Why does this math trick work?

35 by 11 is 385 because 3+5 is 8, so it's the digit in the middle. Same for: 72 by 11 is 792 because 7+2 is 9, so it's the digit in the middle. I see it works because 35 by 10 is 350, or 72 by 10 ...
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2answers
15 views

Speed up divisors' calculation by hand

An exercise such the following one has to be solved by hand during an exam. So, knowing that I need to solve it in about ten minutes, I would like to know if there is a rapid technique to do it. ...
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1answer
61 views

How to parse $2^{1+2^3}$?

I'm fairly comfortable with arithmetic and high school math overall, but I'm having trouble being 100% sure that $2^{\large {1+2^3}}$ should be parsed as 2^(1+(2^3))...
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1answer
26 views

How can we solve $x^a = b \; mod \; n$ equation for big n, a,

I would like to have a method to solve an equation of the type: $x^a = b \; mod \; n$, knowing that n can be decomposed into a product of prime numbers $n = n_1 \times n_2 \times ... \times n_k$ I ...
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1answer
39 views

$x$ generator of $(\mathbb{Z}/p^2\mathbb{Z})^* \implies$ $x$ generator of $(\mathbb{Z}/p^n\mathbb{Z})^*$

As it's indicated in the title, I have to show that $x$ generator of $(\mathbb{Z}/p^2\mathbb{Z})^* \implies$ $x$ generator of $(\mathbb{Z}/p^n\mathbb{Z})^*$, $p \neq 2$. I'm not sure of my proof,...
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0answers
36 views

What method of finding the square root they use in this screenshot?

I saw somewhere a screenshot from a old(?) Russian cartoon with the following math inside. On a screenshot one can see that a student successfully solves 2 exercises on finding square root and ...
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2answers
39 views

which one is larger? 8 factorial to the power of 1/8 or 9 factorial to the power of 1/9

Which one is larger? 8 factorial to the power of 1/8 or 9 factorial to the power of 1/9. Show your work without calculator.
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1answer
66 views

A question in my maths competition that I'm struggling with. [on hold]

I have a list of thirty numbers where the first number is 1, the last number is 30 and each of the other numbers is one more than the average of its two neighbours. What is the largest number on the ...
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1answer
14 views

Closed Form Addition of BCD numbers

Binary Coded Decimal (BCD) number representation is a 4-bit encoding which maps numbers 0-9 to their counterpart binary codes. Addition of BCD numbers can be formulated as follows: z = a + b (If z &...
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0answers
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Spline Space question

Why the spline space $S_{m}^{m}([a,b])=\{s,s \in C^{m}[a,b],s/_{[x_{i},x_{i+1}]}\in P_{m},i=1,..,n\}=P_{m}$? I try to take a $(m-1)^{th}$ polynomial and i prove that is not in to $S_{m}^{m}([a,b])$ ...
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2answers
46 views

Does vedic math trick of squaring numbers have proof of correctness?

Vedic math tricks are usually verifiable, but an empirical proof may be bogus. Vedic squaring method (using duplex), for instance, Does it have a proof of correctness? Trick goes as follows: ...
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1answer
33 views

Prove that $\sqrt{1+a} + \sqrt{1+b} + \sqrt{1+c} \leq 4$ [on hold]

I am trying to prove this inequality but I am having some difficulties. $\sqrt{1+a} + \sqrt{1+b} + \sqrt{1+c} \leq 4$ Edit: sorry i forgot to add a crucial info: $a + b + c = 2 $ and $a,b,c \in R+$
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2answers
54 views

Prove that if $ab$ is a perfect square and $GCD(a,b)=1$, then $a$ and $b$ are perfect squares

How can I easily prove that if $ab$ is a perfect square and $GCD(a,b)=1$ then $a$ and $b$ are perfect squares. I actually managed to prove that this way: if an integer $n$ is a perfect square, then ...
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0answers
26 views

Evaluating polynomial at rational point

When evaluating a polynomial at a rational number, is there an identity which would allow to separately evaluate it at the numerator and denominator? More formally, is there a rule to expand $f(a/b)$ ...
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2answers
50 views

Euclidean division? ( $16=5\cdot 3+1$ vs $16=3\cdot 5+1$)

Is the equality $16=5\cdot 3+1$ the euclidean division of $16$ by $3$ or not ? This question is a point of discord between teachers where some them state that the divisor must be written in the first ...
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0answers
19 views

How do i solve this [closed]

If a relay has a min. Delay of 200ms.and a reset. Time of 360ms.and a plc has a delay of 19ms and a reset time of 11ms. How many times faster is plc. How do I solve this problem.
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2answers
53 views

Is there a term for 'complementary factor'?

Please forgive this incredibly lame question, but if I have factor $n$ of $x,$ and I find its complementary factor $y= \frac xn$, does that complementary factor $y$ have a specific name? I haven't ...
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0answers
30 views

Square root of high number - method

Consider the number $324$, the square root of which is $18$. You first look at the $2$ last digits $24$. You know that your square root has to end with the unit $2$ or $8$ because of the $4$ at the ...
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3answers
215 views

Reverse addition

I have a number 46 which is the result of addition of 12+17+17. Is there a way, given the result 46 and 12 , 17 as the numbers used to get the result, to find out in what combination 12 and 17 was ...
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0answers
10 views

Formula for converting currencies from a to b in relevance to c [closed]

Lets assume a = 1.000000 and b = 0.871992 in relevance to a and c = 0.776907 again in ...
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1answer
41 views

Why $9$ divided by $60$ is the same as $9$ divided by $6$ divided by $10$? [closed]

Why$$9÷60 = 9÷6÷10$$In other words, if you want to break down $60$ into $10$ and $6$, we should say $6\times10$, not $6÷10$?
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2answers
46 views

Explain this fraction equivalence [closed]

Can you explain why $1-\frac{a}{b}$ is the same as $\frac{b-a}{b}$?
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1answer
34 views

How to write a function defined by segments in a formula?

I would like to define a function like $f(x) = 5$ if x is even, and $f(x) = 8$ if x is odd by using a first order logic formula. Is it possible? if yes, how?
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1answer
54 views

$(-1)^3$ has different results when evaluated as $(-1)\times(-1)\times(-1) = -1$ vs $((-1)^2)^{3/2} = 1$. Which is correct?

I know that $$(-1)^3=(-1)\times(-1)\times(-1)=-1 \tag{1}$$ but also $$(-1)^3=((-1)^2)^{3/2}=1^{3/2}=1 \tag{2}$$ So which gives the correct value of $(-1)^3$?
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1answer
80 views

What is the Turing degree of Truth?

First of all by Truth I mean the set $T$ of the Gôdel numbers of the true formulas of first order arithmetic. First order arithmetic is not decidable and $T$ is not decidable, additionally the ...
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1answer
150 views

Using a time machine that can jump to a permutation of the current year

This problem is easy, I provide it just for fun of the community. Like many other mad scientists, I believe that time travel is possible. One of such possibilities was described by a Soviet, ...
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2answers
55 views

Why do Fibonacci Digits always return to either 11 or 14?

I recently posed a question on Code Golf on what I'm terming "Fibonacci Digits", where each number is the sum of the previous two digits, not necessarily the previous two numbers. So, for instance, ...
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1answer
33 views

How does rearrangement work for pulling out factors

Given 10(6*3+2) we can rearrange the equation by pulling out the 3 and getting 10((6*3)/3+(2/3))3 Okay I understand that it ...
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1answer
24 views

Arithmetic speed distance and time

What if the time of departure is 12:15 and time of arrival is 14:45, it’s asking me to find the distance travelled.
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1answer
31 views

Arithmetic question with distance speed and time

If I have a time of departure with is 10:35 and I have an arrival time of 12:55 and the distance 36km how do I calculate average speed? I get the formula of distance speed and time but it says the ...
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5answers
512 views

Famous businessman mathematical puzzle ${}{}$ [closed]

question: A Businessman advertised two job openings for peons in his firm. Two men applied and the businessman decided to engage both of them. He offered them salary of $2000$ rupees per year. $1000$...
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2answers
38 views

Number Systems Containing Non-Unique Additive Inverses

I’ve seen proofs of the uniqueness of the additive inverse of a given element for specified number systems (e.g., the reals, fields in general, etc). Are there known instances of number systems in ...
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1answer
35 views

Arithmetic Progression Question: I have no numbers and I am not sure how to proceed

Three numbers are consecutive terms of a geometric progression. If we add 2 to the second number, the new progression becomes arithmetic. If we add 9 to the third number, the progression becomes ...
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2answers
37 views

Price Calculation Paradox: How to cover tax and fees when these values depend upon one another

I have a real-world math problem pertaining to a pricing formula, a paradox. In this formula, two adjustments are needed, but both depend on knowing the result of each other first. I need to apply ...
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7answers
1k views

What makes the pairs of operators $(-, +)$ and $(÷, ×)$ so similar?

Update My original thoughts are better expressed on this mathoverflow post. Short Version When defining the $-$, $+$, $÷$, and $×$ operators in a functional manner, one can observe that the $(-, +)$...
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1answer
37 views

Minimum number of moves required to obtain chess like coloring.

I've been preparing for a competition and there is this problem that I cannot solve. Can you please help me and also tell me how to do similar problems if they appear in the future? Problem:
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1answer
53 views

Interesting Pattern - Adding or Multiplying Sequential Integers and Then Reducing

I noticed that if you sequentially add integers together, or even multiply them, and then reduce the result, an interesting pattern emerges. ...
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3answers
54 views

Finding the minimum value of $y^2+z^2$

If x,y,z are three integers satisfying $x+y+z=13$ and $xy+xz=42$ ,what is the minimum possible value of $y^2+z^2$ ? How do solve this ? Solution that I thought of : $(x+y+z)/3 >3xyz/(xy+yz+zx)$ ...
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1answer
37 views

How to shorten a line but maintain its angle? [closed]

I have a line that looks like this: to draw this line i have the following: point A: (x,y) point B: (x,y) so for example, i will be given this path: (90,20),(400,300) and then i can draw a line ...
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1answer
39 views

Divide a number in unequal increasing parts according to a dynamic factor

There is a game where you need to gather money from people participating to it and when you have the total you need to divide it in order to put a "reasonable amount" for each of the ...
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2answers
158 views

How is a - (b - c) = c - (b - a) called?

What is the following property of a subtraction operator called? $a - (b - c) = c - (b - a)$ Having a name for this property is important for algebraic structures defined with a subtraction operator ...
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2answers
37 views

How to solve this sequence problem?

$a_1, a_2, a_3\dots\;$ are numbers in a sequence with the condition $$a_{n+1}= a_n + ka_n$$ where k is a constant. If the first number is $20,$ the last is $20000$ and total numbers are $1400.$ ...
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1answer
21 views

What is the approach for solving these kinds of modular arithmetic? [duplicate]

I am new to modular arithmetic. I have gone through a few formulae related to this but I am unable to solve problems like (5^12) mod 23. I am not really bothered about the final answer, but mainly on ...
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1answer
65 views

Prove that $\eta - \omega \notin \mathbb{Q}$ where $\omega$ and $\eta$ are two differents n-th primitive roots $\in \mathbb{C}$

Let $n \in \mathbb{N}$ be a natural number, and be $\omega$ and $\eta$ two differents n-th primitive roots in $\mathbb{C}$. Prove that $\eta - \omega \notin \mathbb{Q}$ My attempt was to follow the ...
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2answers
41 views

any idea…fast tool/way to find what was added?

can anyone please help with a tool or even quicker method? e.g. If I had 163.78 and wanted to make it 200.00 is there a way to find out what was added to make it 200.00? (+36.22 in this case) I ...
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3answers
26 views

solve variable in base

I am asking very petty question. I am confused to solve following equation. Answer should be 9.03. When I calculate, I constantly get different answer (696.4). How would you solve? then I wanna know ...
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2answers
26 views

Problem in calculation of daily expense

I have a simple question. Total amount = 50 USD ...
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3answers
65 views

Find of two arithmetic progressions meet

I was working a problem to find if two AP meet or not and came across the below post Formula to find if two AP meet and in that the formula given by user is $$A_n=A_1+(n−1)d$$ $$B_m=B_1+(m−1)D$$ ...
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0answers
22 views

Formula in summation convention

My friend who is doing some course other than mathematics sent me this problem Can anyone help me figure me out this one. I'm having hard time to understand the problem. Thank you