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Mathematics Stack Exchange
Q&A for people studying math at any level and professionals in related fields

Last digits number theory. - Mathematics Stack Exchange
i have looked at/practiced several methods for solving ex: $7^{9999}$. i have looked at techniques using a)modulas/congruence b) binomial theorem c) totient/congruence d) cyclicity. my actual des...

Bayes theorem tricky example - Mathematics Stack Exchange
In a certain population, 1% of people have a particular rare disease. A diagnostic test for this disease is known to be 95% accurate when a person has the disease and 90% accurate when a person doe...

Probability of getting a full house - Mathematics Stack Exchange
Unfortunately, it's a little difficult to parse your question without LaTeX formatting, which compounds with the fact that I never use that particular notation for binomial coefficients. For those who don't know, a full house is a hand of 5 5 $5$ cards such that 3 3 $3$ of them share the same rank and the remaining 2 2 $2$ also share the same rank. You have 13 13 $13$ choices (2-10, J, K, Q, A ...

What is the number of triples (a, b, c) of positive integers such that ...
$100$ is the number of ordered triples that have product 1000 1000 $1000$. You have failed to account for the condition that a ≤ b ≤ c a ≤ b ≤ c $a\le b\le c$. All of the unordered triples that have three distinct elements have shown up six times, so you have overcounted. Those that have two or three equal elements have been counted ...

What is special about the numbers 9801, 998001, 99980001
$1/(n-1{)}^{2}$ is equal to the series of numbers in increasing order, dropping just the number n-2 ... The examples quoted are for bases 10, 100, 1000 &c. Similar series occur with eg these. These are calculated in base 1000, with leading zeros in each place suppressed. It's true for all bases and their powers.

factorial - Why does 0! = 1? - Mathematics Stack Exchange
Possible Duplicate: Prove $0! = 1$ from first principles Why does $0! = 1$? All I know of factorial is that $x!$ is equal to the product of all the numbers that come ...

How many odd numbers with distinct digits between 1000 and 9999
How many numbers with distinct digits are there between 1000 and 9999. [1] I came up with a solution like this. Since we can't know what numbers have been used, in the tens, hundreds and thousand...

combinatorics - Determine the largest natural number $r$ with the ...
Determine the largest natural number r with the property that among any five subsets with 500 elements of the set {1, 2, …, 1000} there exist two of them which share at least r elements.

elementary number theory - How many digits does $2^{1000}$ contain ...
How many digits does 21000 2 1000 ${2}^{1000}$ contain? Ask Question Asked 14 years, 6 months ago Modified 7 years, 2 months ago

 

 

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