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Monday, August 12, 2024

2024/047) Express the number 2024 as the sum of some positive integers in such a way that the product of these positive integers is maximal.

When we  break a number into smaller parts the product become larger as number of parts becomes larger and each is smaller however no part can be 1 as it shall provide a smaller value. so we can break it into 1012 parts and each is 2 giving a product 2^{1012}.

However there is exception to ir as 2^3 \lt 3^2 so we can group terms of 3 getting 674 3 and left with 1 2 giving a product 3^{674} * 2

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