Note that multiplying c<d by −1 gives −c<−d. So we have a−c<b−d by our previous result. Shouldn't it be c>d in the first place?

cool blog now i know math $

This is great, I think it will help many newbies like me to understand fundamentals and common senses.

I stumbled on a question and it would be great if I could get some help with it. I need to find the sum of (floor(1*sqrt(2)) + floor(2*sqrt(2)) + ... + floor(n*sqrt(2))). To me, this looks really similar to Gauss' property with m = n * sqrt(2), I could be wrong though. It gives me almost right answer with just minor offsets for some values of n. Since, m needs to be an integer, is there any way that we can modify this formula? or is there any other approach you would recommend?

Edit1: https://math.stackexchange.com/questions/1622147/simplifying-sum-of-floor-functions

Edit2: https://mathproblems123.wordpress.com/2020/07/25/sum-of-floors-of-multiples-of-the-golden-ratio/