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Here is a set,

$$A = \{0,3,8,15,24,35,\ldots\}$$

I have to write its set builder notation. I am out of ideas. Can anyone please provide a hint?


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To your edit, $5=2+3\notin A$. –  Asaf Karagila Nov 3 '11 at 7:44
@AsafKaragila: Thanks. I revised the question again. –  Fahad Uddin Nov 3 '11 at 7:51
Note that there are many infinitely many ways to express that set since you need only have a representation that contains those 6 elements (and assuming that it is a non-decreasing order, that it does not contain all other elements less than $35$). –  Dustin Tran Nov 3 '11 at 7:53

2 Answers 2

up vote 5 down vote accepted

Notice that the terms are $1$ less than the perfect squares, so are of the form $ n^2 -1 . $ Then, we can write $$ A = \{ n^2-1 \mid n\in\mathbb{N} \} .$$

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Hope you don't mind my tex edit. –  Rasmus Nov 3 '11 at 9:18
@Rasmus Not at all. Feel free to improve the aesthetics of my posts anytime! –  Ragib Zaman Nov 3 '11 at 9:45

Look at the differences $8-3$, $15-8$, $24-15$, $35-24$.

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