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Number Theory

Divisibility

Divisibility: Level 2 Challenges

         

Is 87985 divisible by 7?

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Victor Paes Plinio by Victor Paes Plinio

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

Abdulrahman El Shafei by Abdulrahman El Shafei

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

Note: 0=020=0^2 is a perfect square.

Satvik Golechha by Satvik Golechha

Given that aa and bb are integers, what can we conclude about the expression

(a2+a+2011)(2b+1)? \big( { a }^{ 2 }+a+2011 \big) ( 2b+1 ) ?

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Krishna Ramesh by Krishna Ramesh

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

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A Former Brilliant Member by A Former Brilliant Member
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