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Browse High School Number Theory
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Diophantine equations.
    Infinite number of primes?
    Testing for primality.
    What is 'mod'?

Finding Mersenne Primes [02/15/2002]
How do I find the first four Mersenne primes?

Finding N Consecutive Composite Numbers [02/26/2001]
How can I find N-1 consecutive numbers that are not prime for any number N greater than 1?

Finding Number of Trailing Zeros in Factorials [01/27/2005]
I noticed a way to compute the number of trailing zeros of a factorial in base 10 or 6 at your site. But that method doesn't seem to work for me in bases such as 4, 8, and 16.

Finding Patterns in Digits [04/29/1998]
How can we find other solutions to problems like 2^5*9^2 = 2592?

Finding Perfect Cube Factors of 10! [04/12/2005]
To find all perfect cubes that are factors of 10!, you don't need to actually evaluate 10!.

Finding Pi [11/14/1997]
What is the quickest algorithm for finding pi?

Finding Prime Factors of Factorials [11/26/2004]
How many factors of 2 are contained in 100! ?

Finding Prime Numbers [11/10/1997]
What is the fastest way to determine if a number is prime?

Finding Products of a Range of Numbers [03/28/2002]
What method or formula is there to solve for the product of a range of numbers?

Finding Pythagorean Triplets [02/02/2006]
Without using the standard a = n^2 - m^2, b = 2nm, c = n^2 + m^2, how can you work out Pythagorean triplets? For example, how could you find triplets where the hypotenuse exceeds one leg by a certain amount?

Finding Pythagorean Triplets Algebraically [04/13/2002]
Is there a way to find Pythagorean triplets of Type I algebraically?

Finding Sets of 7 Prime Numbers That Sum to 100 [05/22/2007]
There are 35 different sets of 7 prime numbers that sum to 100. Of those sets, which has the largest product, and which has the largest number? I'm using trial and error and it's very frustrating. Is there a better way?

Finding Sets of Integers [01/02/2002]

Finding the Exponent with a Modulus [05/24/2003]
I am trying to work out k in the following question: 23^k = 201545 (mod 900001).

Finding the Last Digits of a Large Exponential [01/01/2005]
What are the last five digits of 7777777^7777777?

Finding the Sum of the Factors of a Number [07/25/2007]
Is there a formula to find the sum of all the factors of a given number?

Finding the Two Squares [06/11/2003]
One of Fermat's theorems says that every prime number that yields a remainder of 1 when divided by 4 can be expressed as the sum of two integer squares (e.g.: 97 = 4^2 + 9^2). This theorem was proven by Fermat. What methods are known for determining the two squares?

Find Number Given Divisor and Remainder Information [01/21/2009]
A four digit number N leaves remainder 10 when divided by 21, remainder 11 when divided by 23 and remainder 12 when divided by 25. What is the sum of the digits of N?

Find Remainders: 3^2002/26, 5^2002/26 [09/21/2002]
Find the remainders obtained when 3^2002 and 5^2002 are divided by 26; show that 3^2002 + 5^2002 is divisible by 26.

Find the Flaw [08/02/2001]
I don't understand where the following proof goes wrong...

Find the Monster Mod 11, Mod 2310 [05/07/2003]
Find an integer n between 0 and 2309 with the property that 10^10^10^ 34 = n (mod 2310).

Find the Smallest Number... [10/21/1997]
... that has factors of 1, 2, 3, 4, 5, 6, 7, and 8.

Find the Smallest Number - A Remainder Problem [09/27/2001]
Find the smallest number, M, such that: M/10 leaves a remainder of 9; M/9 leaves a remainder of 8; M/8 leaves 7; M/7 leaves 6; M/6 leaves 5; M/5 leaves 4; M/4 leaves 3; M/3 leaves 2; and M/2 leaves 1.

Find the Smallest Triangle [05/25/2001]
A triangle has sides whose lengths are consecutive integers. Its area is a multiple of 20. Find the smallest triangle that satisfies these conditions.

Find the Solution: r^2 + s^2 = c. [01/28/2003]
Given c, find a^2 + b^2 = c^2.

Find the Unknown Base [06/25/2003]
Two numbers are multiplied to equal another number, which generates a false number statement. What base is it?

Finite Series and Greatest Integers [03/06/2003]
For n a positive integer, let t(n) denote the number of positive divisors of n (including n and 1), and let s(n) denote the sum of these divisors. Prove the following:...

Finite vs. Infinite [07/10/1997]

Finite vs. Rational [9/10/1996]

First Calculation of E [12/18/1997]
How did Euler first calculate the value of e?


Fixed Point and Floating Point Numbers [05/19/2000]
What are fixed point or fixed decimal numbers? How do they differ from floating point numbers?

Floating 2 [06/12/2001]

Floating-Point Binary Fractions [07/19/1999]
How can you represent fractions such as 12.93 in binary? How do computers represent such numbers?

Floor and Ceiling [05/28/2000]
What do 'floor' and 'ceiling' mean in mathematics?

Forming Palindromic Numbers [12/04/1998]

Formula for Connection between Rows of Pascal's Triangle [11/15/2003]
Find a formula connecting any (k+1) coefficients in the nth row of the Pascal Triangle with a single coefficient in the (n+k)th row.

Formula for Counting Triangles [03/16/2000]
How many equilateral triangles of integer-length sides are in an equilateral triangle n units on a side?


Formula for Pythagorean Triples [10/23/1997]


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