An introduction to the ideas of public key cryptography using small
numbers to explain the process. In practice the numbers used are
too large to factorise in a reasonable time.
Lyndon chose this as one of his favourite problems. It is
accessible but needs some careful analysis of what is included and
what is not. A systematic approach is really helpful.
In how many ways can the number 1 000 000 be expressed as the
product of three positive integers?
Make a line of green and a line of yellow rods so that the lines
differ in length by one (a white rod)
The sum of the cubes of two numbers is 7163. What are these
Take any pair of numbers, say 9 and 14. Take the larger number,
fourteen, and count up in 14s. Then divide each of those values by
the 9, and look at the remainders.
Find the smallest numbers a, b, and c such that: a^2 = 2b^3 = 3c^5
What can you say about other solutions to this problem?
Find the smallest positive integer N such that N/2 is a perfect
cube, N/3 is a perfect fifth power and N/5 is a perfect seventh
Show that it is rare for a ratio of ratios to be rational.
Take any prime number greater than 3 , square it and subtract one.
Working on the building blocks will help you to explain what is
special about your results.
How many divisors does factorial n (n!) have?
When if ever do you get the right answer if you add two fractions
by adding the numerators and adding the denominators?