Sum to 1000

Algebra Level 3

The number 10001000 can be written in several ways as a sum of one or more consecutive positive integers, for instance, 1000=10001000=1000 (one summand) or 1000=198+199+200+201+2021000=198+199+200+201+202 (five summands). Find the largest possible number of summands in a representation of 10001000 as a sum of consecutive positive integers.

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