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What does consists of mean exactly, say in an arithmetic progression of length $n$ consists of prime numbers? Are there only prime numbers or must there be at least one prime number in the progression?

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2 Answers

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'consists of' in mathematics means precisely what it means in ordinary language use. If thing $A$ consists of $B$ then it means that the things in $A$ are all $B$. So, if an arithmetic progression consists of prime numbers then all elements in the arithmetic progression are prime numbers.

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If an arithmetic progression of length 3 consists of square numbers, it means that all of its 3 terms are perfect squares.

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