The fractional-part tag has no wiki summary.
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1answer
30 views
How do evaluate an inequality that involves a fractional part?
I am stuck on how to evaluate whether the following condition is true:
Let $\{k\}$ be the fractional part of a real number such that $\{k\} = k - \lfloor{k}\rfloor$.
if $\{\frac{x}{2}\} < ...
0
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1answer
37 views
Fractional part of Median always .5 or .0
If we find the mid value of two integer number,it's decimal part would always contain .5 or .0 exactly
For Example:
(5+10)/2=7 .5
(6+2)/2=4 .0
But,in some coding challenge they asked to calculate ...
0
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4answers
76 views
Simple math: how to extract the fractional portion from a decimal
Mathematically how do I get the cents from a dollar value (ex: $21.99$)?
As a programmer, I would simply convert to a string and grab everything after the decimal... but I would think this would be ...
4
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1answer
148 views
Functional Prime Sums
Let $ f: \mathbb{N} \to \mathbb{N} $ be a number-theoretic function satisfying $ f(xy) = f(x) + f(y) $ whenever $ \gcd(x,y) = 1 $.
How can I prove that
$$
\sum_{\substack{p ~ \text{prime}; \\ p \leq ...
3
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1answer
119 views
How do I get the integer part of a number by using basic arithmetic?
While it is trivial to simply remove the fractional part of an irrational or rational number, and in programming I could just use the floor() or ...
0
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4answers
71 views
Fractional Parts Proof
OK, here are two questions out of Nathanon's Additive Number Theory from the section on fractional parts ($\S$4.4).
I think I'm missing something. I don't understand what there is to prove? Let ...
0
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1answer
71 views
A combinatorics problem refer to this problem?
If i define $f(m,n)=$ $$\sum_{1\leq k\leq mn}\left\{ \frac{k}{m}\right\} \left\{ \frac{k}{n}\right\} .$$
Then prove $$f(m+n,n) - f(m,n) =\frac{n^2-n}{4}$$
for all $m$ and $n$.
This question came ...
16
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3answers
262 views
A sum of fractional parts.
I am looking to evaluate the sum $$\sum_{1\leq k\leq mn}\left\{ \frac{k}{m}\right\} \left\{ \frac{k}{n}\right\} .$$
Using matlab, and experimenting around, it seems to be $\frac{(m-1)(n-1)}{4}$ when ...
