How can we find $\sum_{i=1}^n(n\mod i)$?
Find $\sum_{i=1}^n (n \mod i)$
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elementary-number-theory
modular-arithmetic
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1You are adding things in different groups here. I think what you want is to take a choice of integer representatives in each congruence class $\mod i$ (for example, take the nonnegative integer less than $i$), since it doesn't make sense to add elements $\mod i$ and $\mod j$ when $i\neq j$ – 2012-12-04
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1@BrettFrankel It's possible that the OP intends to in the computer sciencey way, that is, the smallest nonnegative remainder after division (rather than an equivalence class). – 2012-12-04
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0@rschwieb That's the only reasonable conclusion, but I think it's instructive to have it on record that this is not well-defined as stated, and to have the correct formulation of the question appear in at least answers, if not an edit of the original question. – 2012-12-04
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0@BrettFrankel I agree completely with you, and I didn't mean anything by alerting you. I was just trying to feel like I wasn't talking to myself when I made my remark :) – 2012-12-04
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0Elmi - if you find answers to be helpful, you may upvote them (click on the "upwards" arrow to the right of an answer. If you find one answer to be particularly helpful, you can also *accept* one answer per question by clicking in the "greyed out" check-mark to the left of the answer. – 2013-01-15