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Tagged with combinatorics number-theory
1,985
questions
8
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answer
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Does $\frac{(30n)!n!}{(15n)!(10n)!(6n)!}$ count something?
I know a proof that $\frac{(30n)!n!}{(15n)!(10n)!(6n)!}$ is an integer.
The proof goes as:
If a prime $p$ divides $(15n)!(10n)!(6n)!$, then the power of the prime dividing $(15n)!(10n)!(6n)!$ is ...
CommunityBot
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6
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2
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Card shuffling to Even Decks
I have an interesting math question I've developed while playing cards with my family and wonder if anyone has a way to approach the problem.
Say I have n people who each have a deck of cards. Each ...
- 405k
8
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2
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Find an infinite set of positive integers such that the sum of any two distinct elements has an even number of distinct prime factors
I have attempting to solve this using the infinite ramsey theorem, with colouring based on whether the sum of two vertices has an even or odd number of distinct prime factors.
This is leading to an ...
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6
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2
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Construction of an infinite set such that any two number from the set are relatively prime
This question is taken from a contest in India.
Prove that we can construct an infinite set of positive integers of the form $2^{n}-3$, where $n \in \mathbb{N}$, such that any two numbers from the ...
- 33.9k
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3
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Constructing a seven digit number such that one divides the other
This was asked to me by a friend. I tried this problem for a long time, but i couldn't solve it. Seems interesting though.
Prove that it is impossible to construct two different seven digit numbers, ...
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