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product of sum of seven consecutive pairs

Source: 2002 Austria Beginners' Competition p1

October 4, 2022
number theoryalgebra

Problem Statement

We calculate the sum of 77 natural consecutive pairs (e.g. 2+4+6+8+10+12+142+4+6+8+10+12+14) and we will call the result AA, then the sum of the next 77 consecutive pairs (in the example, 16+18+...16+ 18+...) and its result we will call BB, and finally we calculate the sum of the following 77 consecutive pairs and its result we will call CC. Can the product ABCABC be 200232002^3?
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