Ask Dr. Math

High School Archive

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'?

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0 Divided by 0 [11/27/1997]

What is the answer to 0 divided by 0? I think it is undefined...

100 Factorial in Base 6: How Many Zeros? [10/24/2001]

How many zeros are there at the end of 100! in base 6?

Adding Arithmetic Sequences [07/10/1998]

How do you add the numbers from 1 to 5000 without actually doing it or using a calculator? What if you were adding just the odd numbers?

Adding Hexadecimals [07/13/1998]

A complete introduction to the hexadecimal, including sample problems on addition.

Adding in Base 9 and Base 5 [10/21/1997]

In 3rd grade my son is learning how to add in bases other than 10.

Arithmetic in Other Bases [02/25/2002]

I need to know how to write out the steps for addition, subtraction, multiplication, and division in other bases.

Base 12 Fractions [11/05/2001]

I need a simple way to understand how to do and interpret decimals in base 12.

Base 26 [01/27/1997]

In a base 26 number system where the letters of the alphabet are the digits, calculate TWO+TWO in this system and express the answer in base ten. Express 1997 in base 26.

Base 2 Subtraction and Clock Arithmetic [01/26/2001]

We know that computers use the "2's complement" method to do subtraction of base 2 numbers, and that this method works every time, but we have no idea why it works.

Base Number [10/07/1998]

What does base number mean?

Base Number Equivalence Tables [10/30/2001]

My son needs to show tables for base 3 and base 7.

Binary Conversion [01/07/1998]

In an adult computer course we are supposed convert binary numbers to real numbers and binary to hexadecimal.

Binary Subtraction [7/25/1996]

I understand the rules of adding in binary, but how in the world do you subtract?

Binary Subtraction [07/04/2003]

I need help understanding the rules of subtracting binary numbers when the subtrahend is larger then the minuend.

Binary System [5/22/1996]

How do you use the binary system?

Calculating the Last Digit of an ISBN Number [07/15/1998]

How do you calculate the last number in an ISBN number?

Calculator Addition [6/30/1996]

How does a calculator add?

Cardinal and Ordinal Numbers [01/08/1997]

How can 3 be both a cardinal and ordinal number at the same time?

Classifying Numbers [09/06/2001]

Can you tell me about complex numbers, real and imaginary numbers, rational/irrational numbers? I don't understand any of it.

Concepts of Adding in Base 2 [08/18/1998]

I don't understand the whole concept of base 2.

Congruum Problem [04/04/2002]

I have found a reference to Fibonacci and his congruum problem. But something has me stumped...

Converting from Base 6 to 10 and Back [09/26/2001]

I need to know how to convert 2411 in base 6 to base 10.

Counting: Base 6, 12, 16 [5/31/1996]

How do you count in base 6 and base 12? What about base 16?

Decimal To Fraction Conversion [06/25/1998]

I am trying to find a method (one that can be programmed on a PC) to convert the decimal part of a real number to a fraction represented by integers for the numerator and denominator.

Defining Kinds of Numbers [03/21/1997]

Could you please define: perfect numbers, deficient numbers, square numbers, abundant numbers, amicable numbers, and triangular numbers?

Definition of the Signum Function [05/31/2000]

Can you give me a simple definition of the signum function, and any practical examples of its usage?

Diagram for Math Numbers [10/05/1997]

My daughter is doing a tree diagram using terms related to math "numbers." Could you please explain in lay terms what surds are?

Difference Between Zero and Nothing [12/12/1996]

What is the difference between zero and nothing?

Divide by 0 Undefined? [9/10/1996]

When something is divided by 0, why is the answer undefined?

Dividing by 9, 99, 999.... [9/7/1996]

Please explain why dividing x by n 9's (x/99, for example) yields a sequence of n repeating digits.

Divisor Counting [9/24/1995]

A student asks a question about the Math Forum Problem of the Week.

Erdos' Proof of Bertrand's Postulate [3/23/1997]

I am looking for a proof of Bertrand's Postulate (there exists a prime number between n and 2n (n>2)), a.k.a. Chebychev's Theorem.

Even + Even = Even [11/06/2001]

Prove that an even number + an even number = an even number.

Fermat's Last Theorem - Disproof? [05/09/1998]

I would like to ask you whether there is any problem with the following disproof of Fermat's last theorem...

Fermat's Last Theorem: Explanation [11/02/1997]

Please give me some information on Fermat's Last Theorem.

Finding and Factoring Large or Mersenne Primes [02/22/1998]

How do you find extremely large primes (Mersenne Primes) and how do you tell if they are prime? What is the most efficient way of factoring primes?

First Ten Perfect Numbers [12/11/2001]

I have to figure out at least 10 perfect numbers for my homework.

Fraction/Decimal Conversion to Other Bases [08/12/1998]

What are the rules for converting fractions to binary and octal and vice versa?

Frequency of Primes [03/17/1997]

Is there a pattern to describe the frequency of prime numbers?

How can .999999.... equal 1? [03/21/2001]

If .99999999.... goes on forever, wouldn't it be just a little below one?

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