INPUT OUTPUT

**Problem:**
What is *x+y*, *x-y*, *x x y* and *x / y*?

**Excerpt from**
The Algorithm Design Manual:
Any programming language whose level rises above basic assembler supports single- and perhaps
double-precision integer/real addition, subtraction, multiplication, and division. But what if we wanted to
represent the national debt of the United States in pennies? One trillion dollars worth of pennies requires
15 decimal digits, which is far more than can fit into a 32-bit integer.

In other applications *much* larger integers are needed. The RSA algorithm for public-key cryptography
requires integer keys of at least 100 digits to achieve any level of security, and 1000 digits are
recommended. Experimenting with number-theoretic conjectures for fun or research always requires playing with
large numbers.

A Computational Introduction to Number Theory and Algebra by V. Shoup | Algorithms in Java, Third Edition (Parts 1-4) by Robert Sedgewick and Michael Schidlowsky | The Art of Computer Programming : Seminumerical Algorithms by Donald Knuth |

Algorithmic Number Theory : Efficient Algorithms by Eric Bach and Jeffrey Shallit | Introduction to Algorithms by T. Cormen and C. Leiserson and R. Rivest and C. Stein | Introduction to Algorithms by U. Manber |

The Design and Analysis of Computer Algorithms by A. Aho and J. Hopcroft and J. Ullman |

This page last modified on 2008-07-10 . www.algorist.com