Prove That the Following Three Statements About Positive Integers N $n ^ { 3 } + 1$

question 98

Essay

Prove that the following three statements about positive integers n are equivalent: (a) n is even; (b) $n ^ { 3 } + 1$ is odd:
(c) $n ^ { 2 } - 1$ is odd

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Definitions:

Question Marks

Products in a business portfolio that have high growth potential but low market share, often requiring significant investment to grow.

Stars

In the context of the Boston Consulting Group (BCG) matrix, products or business units that have a high market share in a fast-growing industry and are considered to be potential market leaders.

High-Growth Markets

Markets characterized by significantly higher than average growth rates, often driven by new technologies or changing consumer behaviors.

High Share

A significant portion or percentage of the total available market controlled by a particular company or product.