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0
votes
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 $n$.
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16
votes
3answers
264 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 ...
