Ask Dr. Math High School Archive

Dr. Math Home || Elementary || Middle School || High School || College || Dr. Math FAQ

 TOPICS This page:   number theory    Search   Dr. Math See also the Dr. Math FAQ:   0.9999 = 1   0 to 0 power   n to 0 power   0! = 1   dividing by 0   number bases Internet Library:   number theory HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry 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'? Synthetic Division [11/13/1997] Why does synthetic division work? System-Level Programming and Base 2 [05/03/2001] In computer programming, I have a result that contains several values, always a power of 2 (2^2, 2^3, 2^4). If my value is 2^3, 2^4, 2^6 304, how can I tell if 2^3 exists in 304? Systems with More Variables than Equations [12/11/2002] How do I solve a system that has three variables and only two equations, such as 187y + 98x + 45z = 48 and 2y + 9x + 3z = 198? Taylor Expansion [11/21/2001] Can you give me the proof of this statement: arcsin(x) = x + 1/2 (x^3/ 3) + (1/2)(3/4)(x^5/5) + (1/2)(3/4)(5/6)(x^7/7) + ... The basis of the calculation is a Taylor series. A Theorem to Find Lattice Points [6/1/1996] What are the conditions under which the line ax+by=c will contain lattice points? Three Number Theory Questions [10/25/1999] Find the sum of the digits in 4444^4444; find how many times the digit 1 occurs from 1 up to 10,000,000,000; find 3 integers greater than 5^100 that are factors of (5^1985)-1. TI-86 Base Conversion Program [03/19/2002] I have finished writing a program that can convert any number in any base (one-ten) to base ten. Now I am writing a program to convert any number in base ten to a given base. Towers of Hanoi [10/08/2000] Can you prove the formula 2^n - 1 for the least number of moves it takes to move all n discs to another peg in Towers of Hanoi? Trailing Zeros and Zero Factorial [04/07/1998] How many trailing zeros are there for 100! ? Transfinite Arithmetic [10/28/1997] What is transfinite arithmetic? I pretty much know what it means, but I am having trouble applying it to aleph-null. Transfinite Numbers [11/07/1997] I know that Georg Cantor discovered transfinite numbers, but what are they? Triangle Perimeters [12/15/1998] How many triangles with integer sides have a given perimeter? How does the triangle inequality enter into the proof? Triangle Proofs [06/28/1998] The sides of a triangle are a,b,c; prove that (a+b+c)^3 >= 27(b+c- a)(c+a-b)(a+b-c)... Triangular Numbers [07/07/1998] How do you know a number is triangular? How is n/2(n+1) derived? Triangular Numbers [08/23/2003] How do I show that the sum of any two consecutive triangular numbers is always a square number? Triangular Numbers That are Perfect Squares [09/07/99] How can I find and prove a general formula which will give me numbers which are both triangular numbers and perfect squares? Triangular Triples: Means that Are Not So Average [04/28/2012] A student finds several pairs of triangular numbers that average to a third one, and so wonders how many more such triples exist — and how to generate them. With a few inspired variable substitutions and some modular arithmetic, Doctor Jacques responds, then suggests a few new questions to explore. Tribonacci Numbers [11/11/2000] Is there an implicit formula to calculate the nth Tribonacci number? Also, is there a formula to find the sum of the first n Tribonacci numbers? Trick for Numbers Divisible by 3 or 9 [02/24/1998] Proof of a trick for numbers that are divisible by 3 or 9. Twin Prime Numbers [3/11/1996] You know that a prime number is a whole number greater than 1 whose only whole number divisors are 1 and itself. You may not know that there are also such things as twin prime numbers.... Twin Primes [12/24/1997] Are there any studies being conducted on twin primes? Two Prime Numbers with 400-Digit Product [07/29/2006] Find two prime numbers whose product is a 400-digit number. Two's Complement [07/13/1999] What is two's complement and how is it used? Uncountable Infinitude, Illogically Concluded [11/21/2010] If a rational number can be found between any two irrationals, and the set of irrationals are uncountably infinite, does that mean that the rationals are also uncountable? Doctor Peterson points up the flaw in a student's assumption about what to conclude from a failed mapping. Uncountable Numbers [10/20/1997] Why are the real numbers between 0 and 1 uncountable? Undefined Fractions [02/19/2002] Why is a fraction with a denominator of zero called "undefined"? Unique Decomposition of Pythagorean Primes [05/19/2002] Is it true that a Pythagorean prime (i.e., a natural prime that can be expressed as a sum of squares of two integers) can be expressed as a sum of two squares in one and only one way? Unknown Numbers and a Venn Diagram [11/26/2001] The GCF of two numbers is 20 and the LCM is 840. One of the numbers is 120. Explain how to find the other number and use the Venn diagram method to illustrate. Unsolvable and Unsolved Problems [02/19/1998] What's the difference between problems like Squaring the Circle and Goldbach's Conjecture or the Collatz Problem? Uses of Bases Other Than Base 10 [09/28/2004] Why are there different math bases and what would they be used for? Uses of Imaginary Numbers [03/24/1997] Can you tell me a real-life application of imaginary numbers? Using a Calculator in Other Bases [05/16/2000] Can a calculator be used to add non-decimal numbers? For example, 27 octal + 65 octal. Using Algebra to Find Lucky Numbers [12/26/2007] A lucky number is a positive integer which is 19 times the sum of its digits. How many different lucky numbers are there? Using Binomial Expansion to Evaluate [2 + sqrt(3)]^50 [11/29/2006] I've used a computer to evaluate [2 + sqrt(3)]^50 and the answer is extremely close to being an integer. I've tried various expansions of the expression to try and determine why it's so close to an integer, but haven't gotten anywhere. Do you have any idea why? Using Mod to Find Digits in Large Numbers [12/10/1996] Find the last two digits in 1996^1996. Using Modular Arithmetic to Find Remainders [10/21/2004] What is the remainder when 2^(2^405) is divided by 23? Using Modular Arithmetic to Test Divisibility of Large Numbers [08/30/2008] Prove that 55^62 - 2*13^62 + 41^62 is divisible by 182. Using Weighted Criteria to Make Decisions [07/18/2008] I have three employees who have each worked different numbers of days and learned different numbers of skills in that time. How can I decide who is the most effective employee by weighting those two factors? USSR Math Olympiad Puzzle [04/16/2003] Prove that no matter what string you start with, the letters at the corners of the triangle are either all the same or all different. To what other numbers could you change the 'string of 10 letters' and still have the assertion be true? Variable Within and Outside an Exponent [07/29/1997] Solve for t: d = a*t + b*e^-(c*t) where a, b and c are constants and e is the exponential. Page: [<]

Search the Dr. Math Library:

 Search: entire archive just High School Number Theory Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

[Privacy Policy] [Terms of Use]

© 1994-2014 Drexel University. All rights reserved.
http://mathforum.org/
The Math Forum is a research and educational enterprise of the Drexel University School of Education.