0
votes
0answers
24 views

Coprime number factoring [closed]

Given an great integer $n$ (eventually $n+1$, $n+2$...) Find a factoring (or an algorithm for factoring) $n=f_1 \cdot f_2 \cdot f_3$, where $f_1$, $f_2$, $f_3$ are coprime and similarly. Example : ...
2
votes
3answers
72 views

Factoring/approximating an apparently simple formula

Does anyone know if the following formula can be factorized or approximated: $a^3 + b^3 + c^3 + a^2b + ab^2 + a^2c + ac^2 + b^2c + bc^2 + abc$ It looks a lot like $(a + b + c)^3$, except for the ...
15
votes
4answers
713 views

Calculating $\sqrt{28\cdot 29 \cdot 30\cdot 31+1}$

Is it possible to calculate $\sqrt{28 \cdot 29 \cdot 30 \cdot 31 +1}$ without any kind of electronic aid? I tried to factor it using equations like $(x+y)^2=x^2+2xy+y^2$ but it didn't work.
6
votes
1answer
265 views

Find the value of $x^3-x^{-3}$ given that $x^2+x^{-2} = 83$

If $x>1$ and $x^2+\dfrac {1}{x^2}=83$, find the value of the expression$$x^3-\dfrac {1}{x^3}$$ a) $764$ b) $750$ c) $756$ d) $760$ In this question from given I tried to ...
2
votes
3answers
2k views

How can I use prime factorization to find a cube root?

This is based on a lesson at Khan Academy that I didn't understand. In the lesson, the instructor uses the number 512 as an example and the entire prime factorization consists of three groups of ...
2
votes
2answers
83 views

Multiplying over Subtraction

I'd like to take maths seriously but I'm not that great at it, so I decided to learn at home. I know this is pretty basic, but as I said, I'm pretty bad at maths, haha. The worksheet gives me this ...
2
votes
3answers
333 views

Factoring extremely large integers.

The question is about factoring extremely large integers but you can have a look at this question to see the context if it helps. Please note that I am not very familiar with mathematical notation so ...
1
vote
1answer
76 views

Factorizing Composites

Say $N=AB$ where $A$ and $B$ are primes. We write: $$A=a+x,\qquad B=a-x.$$ That is, $$a=\frac{A+B}{2};\qquad x=\frac{A-B}{2};$$ $A$ and $B$ are odd numbers. Therefore $A+B$ and $A-B$ are even. And ...
2
votes
4answers
219 views

Find largest integer $x$ such that $3^x$ is a factor of $27^5$

Is the following solvable using just arithmetic rather than a calculator, and if so, how? Which of the following numbers is the greatest positive integer x such that $3^x$ is a factor of $27^5~$? ...