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 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'? Congruence of Integers [08/10/1998] Can you help me find the remainder when 5 to the power of 1001 is divided by 6...? Conjecture About Squares of Consecutive Numbers [08/28/2001] When any two rational numbers whose absolute values are 1 apart are squared, the difference of the squares is equal to the absolute value of the sum... Conjectures vs. Hypotheses [01/12/1999] What is the difference between the terms 'conjecture' and 'hypothesis'? Should the Riemann hypothesis be the Riemann conjecture? Connecting the Dots [03/14/1999] If you have a few dots on a page, how many lines does it take to connect them all to each other? Consecutive Composite Numbers [07/05/2002] Find 1000 consecutive composite numbers. Consecutive Composite Numbers [06/07/2005] Is it possible to find m consecutive composite numbers where m is any natural number? Consecutive Fibonacci Numbers Relatively Prime [11/17/2001] Prove two consecutive Fibonacci numbers are relatively prime. Consecutive Integers [02/10/1999] Can the product of four consecutive integers be a perfect square? Consecutive Integers, Divisible by the Sums of Their Digits [05/20/2002] Find the first three consecutive integers greater than 10, each of which is divisible by the sum of its digits. Consecutive Non-Prime Integers [2/17/1996] For any integer n > 1 there exist n consecutive non prime integers. I have taken n = 4 and then used 24,25,26,27 as a specific example. However, for n large I don't see how this can hold. Continued Fraction for Tan(x) [11/03/2000] Can you tell me why the "infinite continued fraction representation" for the tangent function works? Continued Fractions [10/07/1997] Exactly what are "continued fractions"? Convergence of a Prime Sequence [02/10/2002] We know the sum(1/n) (n=1, infinity) does not converge, but what about sum(1/p) where sum is over prime numbers only. Does it converge? Converting a Base 2 Log [01/31/2002] 2147483647 is one less than what power of 2? Converting a Fraction Into a Continued Fraction [11/29/2003] I know how to convert a continued fraction into a standard fraction, but I can't figure out how to to the other way. How can I convert a standard fraction into a continued one? Converting any Number Base to Another [05/11/2001] Is there a particular technique for the conversion of any number base into any other base? I also need information on basic numeric calculations within a base 5 system. Converting Base Numbers Directly Without Using Base 10 [01/26/2004] How do you convert from one base to another without going through base 10? How do I go from base 3 to base 7, for instance? Would the same algorithm work to go from base 5 to base 12? Converting Bases [9/5/1996] How do I convert from one base to another - i.e. decimal to bin, hex, and oct? Converting Bases [12/21/1997] How do you convert hexadecimal, binary, and decimal numbers? Converting Bases Without Going through Base 10 [09/04/2002] Is there a way to convert between bases without going through base 10? Converting Binary and Decimal to Hexadecimal and Back [08/12/2001] How do you convert binary and decimal numbers to hexadecimal and vice versa? Converting Binary to and From Decimal [06/16/1999] Can you show me how to convert base 2 numbers into base 10 and vice- versa? Converting Decimal Numbers from Base 2 to Base 8 or 16 [02/20/2009] I understand converting binary to octal or hexadecimal in general, but am curious how you handle the decimal portion of a number. Converting Directly from Base to Base [04/01/2001] Is there a way of reducing the representation of a natural number from one base to another directly without reducing to base 10 first? Converting Floating Decimals to Other Bases [11/27/2003] I know how to convert integers to other bases. But how do I convert the decimal parts of non-integers such as 123.5 or 8.4444....? Converting Fractions from Binary to Decimal [02/25/2002] Can you explain how to convert binary fractions to decimal numbers, e.g. 0.00011001100110011001...? Converting from Base 10 to Base 3 [02/12/2002] How do you convert a base 10 number (example 2315) to base 3? Converting from One Base to Another [10/28/1996] How do you convert a number base 9 to base 4? from base 9 to base 10? Converting Negative Decimals to Hexadecimal [05/30/2001] Using a calculator I can get conversions like - 16 = F0, but what I need to know is how to get to F0 from - .16 Converting Numbers: Binary to Decimal [11/20/1997] I just cannot convert from binary to decimal and back again. Converting Repeating Decimals from Base X to Base Y [10/02/2009] How do I convert a repeating decimal from base 9 to base 6? For example, 0.54444444... (base 9) to base 6. Converting to Base 16; Place Value Chart [03/22/1998] How do you convert numbers to base 16 numbers? Converting to Binary [05/27/2001] Converting the number .78125 to its binary equivalent. Coprimes in Fermat's Last Theorem [06/03/1999] Why are (z-x)/2 and (z+x)/2 coprime in Fermat's Conjecture when n = 2? Countability of Rational and Irrational Numbers [01/30/2001] When speaking of countability of numbers, which has more, rational or irrational? Counting Digits [03/13/2002] How many times does each digit appear when counting from 1-1000 and 1- 10000 (including zeros)? Counting Even Digits in Three-Digit Numbers [10/24/2004] How many 3-digit numbers are there in which the number of even digits is even? Counting in Base 5 [03/02/2004] How do I count from 1 to 7 in base 5? Counting Odd Coefficients [05/27/1998] If (1+x)^100 is multiplied out, how many of the coefficients are odd? How would you generalize? Counting Positive Rational Numbers [09/09/2001] In Hardy's book _Pure Mathematics_ he gives a formula for counting the positive rational numbers p/q when they are arranged in a triangular matrix and counted down diagonally from the top row... how can it be proved for all such numbers? Page: [] [last>>]

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