Tagged Questions

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

98 views

Stuck on simple proving

Prove that $\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{1}{5}+\frac{1}{6}-\cdots-\frac{1}{2009}+\frac{1}{2010}<\frac{3}{8}$ Oh my, I feel embarrased for not knowing how to solve such an elementary ...
185 views

It has been so long since I have done division inside of radicals that I totally forget the "special rule" for for doing it. -_- For example, say I wanted to divide the ...
206 views

Primes in nonstandard models of PA

What is known about prime numbers in nonstandard models of PA? Restricted to true natural numbers the sets are identical, but does there always exist nonstandard primes? Can we explicitly define one ...
287 views

How to compute these GCD's?

Please suggest me how to compute the GCD of theese really big numbers : GCD of $2^{120547564397}-1$ and $2^{356946681940}-1$ GCD of $2^n-1$ and $n!$ where $n=3^{19}$ Thanks to Bill Dubuque's ...
285 views

Division with 4 digit number in denominator

I've got a question in my task sheet. The question is as follows. $$\frac{43\cdot93\cdot47\cdot97}{3007}=X$$ Find the exact value of $X$. I've tried a lot, but couldn't find easier way to do it ...
238 views

I am trying to figure out how to add negadecimal numbers by hand. I can add normal decimal numbers using an algorithm I learned in kindergarten: start with the least significant digits, add them, ...
121 views

How to factor 5671?

The other day I wanted to factor 5671 in my head. (It turns out to be $53\cdot107$, but I did not know this at the time.) I quickly ruled out the easy divisors, 2, 3, 5, 7, 11, and 13. At this point ...
170 views

What is the square root of $i^4$?

What is the $\sqrt{i^4}$? $i^4$ = $(i^2)^2$ So is $\sqrt{i^4}$ = $\sqrt{(i^2)^2}$ = $i^2$ = $-1$? Or is $\sqrt{i^4}$ = $\sqrt{1}$ = $1$? When I plug it into my TI-89 Titanium, I get $1$. Edit: I ...
60 views

I am confused about some exponent behavior. $$(-2)^{7.6} = (-2)^{\frac{76}{10}} = ((-2)^{76})^{\frac{1}{10}} = ((-2)^{\frac{1}{10}})^{76}$$ Is there something wrong in this logic? When I plug the ...
2k views

rules for rounding (positive and negative numbers)

I'm looking for clear mathematical rules on rounding a number to n decimal places. Everything seems perfectly clear for positive numbers. Here is for example what I found on math.about.com : Rule ...
47 views

How do I append an integer to the left of another integer?

For example: . is my append operator f(x,y) = |x| . |y| f(1,45) = 145 f(233,10) = 23310 f(8,2) = 82 f(0,1) = 1 This is a trivially easy problem to ...
224 views

Is there a log-space algorithm for divisibility?

Is there an algorithm to test divisibility in space $O(\log n)$, or even in space $O(\log(n)^k)$ for some $k$? Given a pair of integers $(a, b)$, the algorithm should return TRUE if $b$ is divisible ...
290 views

A “fast” way to find the sum of the sequence $5,5.5,5.55,5.555,5.5555,\ldots$ (20 terms)

My initial approach is diving the whole sum by $9$ and taking the common $5$ out which gives $$\frac{5}{9}[(10-1)+(10-0.1)+(10-0.01)+\cdots + (10-10^{-19})]$$ after some algebra this could be reduced ...
757 views

Chinese Remainder theorem with non-pairwise coprime moduli

Let $n_1,...,n_k \in \mathbb{N}$ and let $a_1,...,a_k \in \mathbb{Z}$. How to prove the following version of the Chinese remainder theorem (see here): There exists a $x \in \mathbb{Z}$ satisfying ...
856 views

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How can I write an algorithm to perform the following calculation exactly? (references accepted)

Given natural numbers $N, K, m, C$, with $3^{m/3}K>C$, I want to be able to write an algorithm to exactly compute the number $$\left\lceil \log_3 \left(\frac{N}{3^{m/3}K-C}\right) \right\rceil$$ ...
486 views

Long division notation (census of nations)

The Wikipedia article on long division explains the different notations. I still use the European notation I learned in elementary school in Colombia. I had difficulty adapting to the US/UK notation ...
375 views

Can two sets have same AM, GM, HM?

Can two set of numbers(same size) have same arithmetic , geometric, and harmonic mean ? When I say different set they must differ by at-least $1$ element and also what if set is not be of distinct ...
9k views

How to convert a hexadecimal number to an octal number?

How can I convert a hexadecimal number, for example 0x1A03 to its octal value? I know that one way is to convert it to decimal and then convert it to octal ...