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Number Theory
# Divisibility

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Is 87985 divisible by 7?

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Victor Paes Plinio**

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Find the smallest positive multiple of nine containing only even digits.

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A K**

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How many perfect squares have the property that all of their digits are equal?

**Details and Assumptions**

- For this question, \(0=0^2 \) is also a perfect square.

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Satvik Golechha**

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Given that \(a\) and \(b\) are integers, what can we conclude about the expression

\[ \big( { a }^{ 2 }+a+2011 \big) ( 2b+1 ) ? \]

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Krishna Ramesh**

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\[\frac{(n+2)!}{(n-1)!}\] The above fraction is divisible by which of the following?

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Brilliant Member**

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