2019 AMC 12A 第 4 题

The integers are allowed to be negative

Adding $-44, -43, \ldots, 44$ contributes $0,$ so extend the run just past $45$

Negative integers are allowed. The integers from $-44$ to $44$ sum to $0,$ so the integers from $-44$ to $45$ sum to $45.$

This run has $45 - (-44) + 1 = 90$ integers. Conversely, if $L$ consecutive integers have sum $45,$ then twice their sum is $L$ times an integer, so $90$ is a multiple of $L.$ Hence $L\le90,$ proving that this run is longest.

Thus, the correct answer is D.