2
votes
2answers
60 views

Proper decimal fraction for $\frac{4n+1}{n(2n-1)}$

Assume I have a function $f(n) = \frac{4n+1}{n(2n-1)}$ with $n \in \mathbb{N} \setminus \left\{ 0 \right\}$. The objective is to find all $n$ for which $f(n)$ has a proper decimal fraction. I know ...
1
vote
3answers
48 views

Irreducibility of gcd/lcm or lcm/gcd

Consider two irreducible fractions: $r_{1} = \frac{p_{1}}{q_{1}}$ $r_{2} = \frac{p_{2}}{q_{2}}$ Are these two fractions: $r_{3} = \frac{\text{gcd}\left(p_{1}, p_{2}\right)}{\text{lcm}\left(q_{1}, ...
1
vote
3answers
42 views

Reducing a fraction, divisibility and indeterminate symbol

Quick question about validity, just to make sure. When I have a fraction in a form: $$\frac{3a + 3b}{a+b}$$ and I extract the common factor 3 out to get: $$\frac{3(a+b)}{a+b} \;=\; 3\frac{a+b}{a+b}$$ ...
1
vote
0answers
32 views

Computability of division of large numbers

What is the largest computable mathematical division in terms of the number of digits that can be handled by a typical desktop computer using the best available big number libraries, assuming input is ...
8
votes
4answers
740 views

Remainder when $20^{15} + 16^{18}$ is divided by 17

What is the reminder, when $20^{15} + 16^{18}$ is divided by 17. I'm asking the similar question because I have little confusions in MOD. If you use mod then please elaborate that for beginner. ...
2
votes
3answers
168 views

Proving that $\frac{n+1}{2n+3}$ is irreducible

I am trying to solve the following problem: Prove that the following fractions are irreducible for any n (n is a natural number and it cannot be null). $\frac{n}{n+1}$ $\frac{n+1}{2n+3}$ ...
4
votes
3answers
123 views

Divide with remainder $\frac{x^2}{x^2 + x + 2}$

I am having a hard time long dividing: $$\frac{x^2}{x^2 + x + 2}.$$ Could someone please show a step by step way to divide this, as I can only get it down to : $1 + \frac{x^2}{x + 2}$. Thank you ...