Questions on basic arithmetic, e.g. addition, subtraction, multiplication, division, powers, radicals, etc.

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0
votes
1answer
23 views

How to prove that $(a-b) \mod N = a \mod N + ((-b) \mod N)$?

I've gone through the similar post Modulo of a negative number . But that post is not about proof and I'm asking for the proof in general. This question is another follow up question of my previous ...
2
votes
1answer
21 views

Absolute value of infinite series sum

How does it come about that $$\left|\Sigma_{n=-N}^{N}c_n(f)e^{inx} - \Sigma_{-\infty}^{+\infty} c_n(f)e^{inx}\right| = \left|\Sigma_{|n|>N} c_n(f)e^{inx}\right|?$$ What happens with the $n$-index? ...
0
votes
1answer
22 views

Absolute value of a complex sum

How can $|{\cos(n x)+i \sin(n x)}|$ = 1 (for $n$ and $x$ positive)? I'm not very good with complex numbers yet, so I would appreciate if someone could please explain how this absolute value comes to ...
14
votes
7answers
1k views

Why do remainders show cyclic pattern?

Let us find the remainders of $\dfrac{6^n}{7}$, Remainder of $6^0/7 = 1$ Remainder of $6/7 = 6$ Remainder of $36/7 = 1$ Remainder of $216/7 = 6$ Remainder of $1296/7 = 1$ This pattern of ...
1
vote
0answers
20 views

How to check that numbers “a” and “ b”, a digit at a position “i” from number “b” is less or equal than the digit at position “i” at number “a”?

How to check that for given natural numbers "a" and " b", a digit at a position "i" from number "b" is less than the digit at position "i" at number "a" without iterating digit by digit? e.g. for ...
-1
votes
1answer
28 views

Line rental puzzle [on hold]

If a device line rental is 155.88 for a year plus 5.99 p&p plus 2.50 for first month (30total for year) =164.37 And offer is with 50 cashback So, total year spend is: 155.88 line rental 5.99 ...
0
votes
1answer
45 views

A vessel contains $x$ amount of milk out of which $y$ amount is taken out and replaced with water $n$ times.

There is a formula in my book for questions of type, A vessel contains $x$ amount of milk out of which $y$ amount is taken out and replaced with water. After $n$ such operations what will be the ...
1
vote
1answer
29 views

How to solve problems on alligation and mixture when three types are given?

Suppose there are three qualities of rice, A(1 dollar per Kg), b(2 dollar per Kg) and C(3 dollar per Kg). The salesmen want to mix these in a certain ratio a:b:c so as to make the price 2.5 dollar per ...
-1
votes
0answers
23 views

this is a question of class 7 from integers [on hold]

A water tank has steps inside it. A monkey is sitting on the topmost step (i.e., the first step). The water level is at the ninth step. (i) He jumps 3 steps down and then jumps back 2 steps up. In how ...
2
votes
1answer
45 views

Given $N$, is there a formula for $card( \{(m,n)\, s.t.\, m\cdot n \leq N \} )$?

The formula is also equivalent to : $$ \sum_{m=1}^N \left \lfloor \frac{N}{m} \right \rfloor $$ An interpretation would be to count the discrete rectangles with total area inferior to N. But aside ...
-7
votes
0answers
45 views

i need help for my homework [on hold]

If 5 is one factor of negative 20 what is the other factor
3
votes
5answers
67 views

Simplify Square Root Expression $\sqrt{125} - \sqrt{5}$

$\sqrt{125}-\sqrt5$ simplify it. I thought it would be $\sqrt {5\cdot5\cdot5}-\sqrt 5$ which would be the square root of 25 which is 5 but it is not. Can you show how to simplify this?
1
vote
2answers
37 views

Exponential function negative: $\left(\frac{81}{4}\right)^{1/4}\left(\frac{1}4\right)^{-3/4}$

This is another example. $\left(\dfrac{81}{4}\right)^{1/4}\left(\dfrac{1}4\right)^{-3/4}$ Multiply on both sides equals $\dfrac{81^{1/4}}{4^{1/4}}\cdot \dfrac{1^{-3/4}}{4^{-3/4}}$ This should be ...
0
votes
2answers
52 views

Elementary Substitution in Solving Equations - Why it works

To solve a system of linear and certain non-linear equations, the substitution method is widely used by elementary and high school students. As explained here, to solve this simple system of linear ...
-1
votes
1answer
11 views

Order of operation to get total

Does anyone know the answer for this equation: $$((6.2 * 4) * ((0.00019106 * 2,715,297.4673) + (0.00226263 * 4,500) + 0.55))\\ * (1 + 0.1 + 0.02 ) / 150 * 10 = ?$$ I also do not understand how it is ...
1
vote
1answer
77 views

Is it possible to define $x+x+x+x…x$ times? [duplicate]

Is it possible to define $x+x+x+x...x $ times? I need to compute its derivative. It differs from the derivative of $x^2$. It evaluates to $x$ via sum of derivatives.
0
votes
0answers
22 views

With a sequence $\{B_n\}$ and a function defined on all of its elements, what are the spaces between the outputs of the function?

I have a sequence $\{B_n\}$ and a function defined for every member of that sequence: $f(B_i,C_j)=a_j^i$ (Where the spaces between any two adjacent $C$'s is always constant). Such that the following ...
3
votes
2answers
86 views

Explaining elementary arithmetic in terms of group theory

It is possible to explain elementary arithmetic in terms of group theory? Addition and subtraction seem to be fine using $(\mathbb{R},+)$ but when it comes to multiplication and division it does not ...
1
vote
1answer
30 views

Possible to turn any in-fix expression into post-fix with all values on one side?

I remember hearing (correctly or not) that any thing in in-fix notation can be made into post-fix notation with all of the values put on the stack before any operation. $a + b + c \implies a\,b\,c + ...
1
vote
1answer
47 views

How many binomials are divisible by $p$?

Let $N$ be a interger (maybe $10^{15}$) and $p$ be a prime number less than $N$. How many binomials ${n}\choose{k}$, where $n<N$, divisible by $p$? we already know that ${pm}\choose{pn}$ $\equiv$ ...
1
vote
0answers
60 views

Best intro to Fundamentals of Mathematics? [closed]

If you like mathematics it's likely that you also want to have the most solid foundations in number theory and analysis possible. I have just finished Elliott Mendelson's book Number Systems and the ...
0
votes
2answers
89 views

How do you solve the equation $6g + 8 = 9g - 25$? [closed]

$6g+8=9g-25$ Can you simply solve for $g$? I'm having trouble with the steps.
9
votes
13answers
655 views
+200

What is $0\div0\cdot0$?

We all know that multiplication is the inverse of division, and therefore $x\div{x}\cdot{x}=x$ But what if $x=0$? $0\div0$ is undefined so $0\div0\cdot0$ should be too, but whatever happens when we ...
1
vote
2answers
34 views

How to evolve an expression with two denominators

The task is to simplify the expression: $\displaystyle\frac{f(x+h)-f(x)}{h}$ when $\displaystyle f(x) =\frac{1}{x}$. I don't know how to do this since I get to the step ...
3
votes
2answers
87 views

How to replace addition with multiplication to find the next integer value?

Sorry in advance for my lack of mathematical knowledge, I am very new to it. Yesterday, I posed this question to myself: "In a world without addition or subtraction, how could we derive the next ...
0
votes
0answers
25 views

Order of evaluation of a simple term

If, for example, $a=14$, $b=2$ and $c=7$ and I'm working to (say) three decimal places, should I evaluate the term$$a\frac{b}{c},$$ in the order $$a\left(\frac{b}{c}\right)$$ ...
0
votes
2answers
34 views

Proportions manipulation [closed]

Knowing that \begin{equation}\frac{a}{b}=\frac{c}{d}\ \ , \ \ \frac{a'}{b'}=\frac{c'}{d'}\end{equation} find the condition that the sums \begin{equation}a+a',\ b+b',\ c+c',\ d+d',\end{equation} ...
-1
votes
1answer
55 views

Find the number of six-digit numbers that can be formed

find the number of six-digit numbers that can be formed using the digits from the number 112 233. If these numbers are arranged in ascending order,find a.) the largest number. b.) the 30th number. ...
-2
votes
0answers
39 views

How to multiple and divide large decimal numbers? [closed]

I need to know how to multiple and divide large numbers especially decimal numbers on paper. It would help if you could demonstrate a simple calculation using a basic sure method then scaling it up to ...
2
votes
2answers
72 views

Simple Puzzle: A Matter Of Time

I am trying to solve a simple puzzle: Fifty Minutes ago if it was four times as many minutes past three O'clock, how many minutes is it to six O'clock. I tried solving it: Let x be the minutes past ...
1
vote
3answers
82 views

Find numbers $\overline{abcd}$ so that $\overline{abcd}+\overline{bcd}+\overline{cd}+d+1=\overline{dcba}$

Find the numbers $\overline{abcd}$, with digits not null that satisfy the equality \begin{equation}\overline{abcd}+\overline{bcd}+\overline{cd}+d+1=\overline{dcba}\end{equation} where ...
12
votes
5answers
267 views

Is $1 : 7 = 1 / 8$ or is it $1/7$?

In a certain (non-mathematical) Stack Exchange, when I wrote $n : m = n / m$ where $n$ and $m$ are positive integers, one of the moderators said "No! $n : m$ is usually the notation for "$n$ parts in ...
22
votes
3answers
5k views

Why does this age calculation trick work?

The trick works like this: Take the current date in the format yyyymmdd and subtract it with your date of birth taken in the same format. Drop the last four digits to get your age. For example, I was ...
3
votes
3answers
59 views

Negative roots of a cubic equation

Under what conditions will the cubic equation $ax^3 + bx^2 + cx + d$ where $a,b,c,d \in \mathbb R$ yield roots which have negative real parts? (All roots must have negative real parts) Motivation: I ...
0
votes
0answers
23 views

How many grams of coating is being yield per volume width?

The cylinder is 8.00 inches in diameter and 4.940 inches in width. 1.500 inches in width has a volume of 15. 3.440 inches in width has a volume of 12. The total grams of coating yield from the both ...
1
vote
2answers
65 views

Does $k\cdot x < y$ imply that $x \ne y$?

Sorry if the question is trivial, but I have trouble getting my head around it. To keep short, does $\forall k \in \mathbb Z^*, \forall (x, y) \in \mathbb Z^2, k\cdot x < y \implies x \neq y$? ...
6
votes
4answers
608 views

Last 10 digits of the billionth fibonacci number?

I want to compute the last ten digits of the billionth fibonacci number, but my notebook doesn't even have the power to calculate such big numbers, so I though of a very simple trick: The carry of ...
1
vote
1answer
46 views

Finding remainder of negative number

Recently my colleague ask one mathematical question which is, What is the quotient and remainder of $(-29)/7$? and my answer was that quotient is $4$ and remainder is $-1$ and he told me I'm ...
9
votes
6answers
520 views

How to prove that $7^{31} > 8^{29}$

How can I prove that $7^{31}$ is bigger than $8^{29}$? I tried to write exponents as multiplication, $2\cdot 15 + 1$, and $2\cdot 14+1$, then to write this inequality as $7^{2\cdot 15}\cdot 7 > ...
0
votes
0answers
26 views

Properties of exponentiation proof

I'm trying to prove the following: "Let $x, y$ be non-zero rational numbers, and let $n,m$ be integers. Then we have $x^n x^m = x^{n+m}$." I've managed to prove by induction the case $n,m \geq 0$ ...
0
votes
0answers
7 views

Moving average where periods have unequal # of samples

I'm trying to compare a simple moving average approach to one that normalizes by the number of samples in a period to determine which is "more correct." Here's a representative piece of the data: ...
1
vote
2answers
37 views

Confused about proof of division

I thought I was familiar with the regular Euclidean algorithm, but I am having trouble understanding a step in this proof from my notes, I am looking for any clarification. Theorem Let $a, b \in ...
-2
votes
2answers
65 views

Mathematical induction problem. Let $S_{n}=\left (3+\sqrt{5}\right)^{n}+\left(3-\sqrt{5}\right)^{n}$ [closed]

Let $S_{n}=\left (3+\sqrt{5}\right)^{n}+\left(3-\sqrt{5}\right)^{n}$then, by mathematical induction, show that $S_{n}$ is an integer. Also, prove that the next integer greater than ...
-4
votes
1answer
50 views

Add or subtracts 1 to 9 numbers and get the answer 100 [closed]

so the question is that we have add or subtract numbers from 1 to 9 and the answer should be 100. (Note: The numbers shouldn't repeat). so what is the solution to this problem? Please answer this ...
4
votes
3answers
443 views

Unusual result to the addition

Question: Prove that (666... to n digits)^2 + (888... to n digits)=(444... to 2n digits) My way: I just proved the given equation for three values of n and written at the bottom. "Since the ...
-4
votes
3answers
36 views

Finding the remainder while dividing negative numbers? [closed]

What is the remainder when dividing $-29$ by $8$?
4
votes
4answers
91 views

$(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3=24xyz$?

The question given is Show that $(x+y+z)^3-(y+z-x)^3-(z+x-y)^3-(x+y-z)^3=24xyz$. What I tried is suppose $a=(y+z-x),\ b=(z+x-y)$ and $c=(x+y-z)$ and then noted that $a+b+c=x+y+z$. So the ...
2
votes
2answers
87 views

How to show this fraction is not an integer

Suppose $k\geq 2$ is an integer. I want to show $$\frac{1+k+k(k-2)}{1+\frac{k-1}{k}+\frac{(-1-\sqrt{k-1} )^2}{k(k-2)}}$$ is not an integer. It is equal to $$\frac{(k-2) k (k^2-k+1)}{2 (k^2-2 ...
1
vote
5answers
147 views

If $a+b+c+d=1$ then why is the maximum value of $(a+1)(b+1)(c+1)(d+1)$ is ${\left(\frac{5}{4}\right)}^4$?

What I know is that for equations of type $x+y=8$, $xy$ attains its maximum value when $x=y$ and this can be proved by either solving the quadratic equation with completing the squares or finding the ...
4
votes
1answer
132 views

How do I find two integers - $x$ and $y$ - whose values satisfy the expression $x^2 + y^2 = z$, where $z$ is a perfect square?

I watched a YouTube video of an episode of Who Wants To Be A Millionaire?, in which a contestant was presented with a list of perfect squares. He was asked to choose the number that was also the sum ...