BMO Round 1, 2018

Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Helen divides $365$ by each of $1, 2, 3, \dots , 365$ in turn, writing down a list of the $365$ remainders. Then Phil divides $366$ by each of $1, 2, 3, \dots , 366$ in turn, writing down a list of the $366$ remainders. Whose list of remainders has the greater sum and by how much?

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