tear a sheet from a numbered notebook
Source: 2021 Austrian Mathematical Olympiad Junior Regional Competition , Problem 1
September 12, 2021
algebraSum
Problem Statement
The pages of a notebook are numbered consecutively so that the numbers and are on the second sheet, numbers and , and so on. A sheet is torn out of this notebook. All of the remaining page numbers are addedand have sum .
(a) How many pages could the notebook originally have been?
(b) What page numbers can be on the torn sheet?(Walther Janous)