Write 100 as the sum of two positive integers, one divisible by 7 and the other divisible by 11.
Then find formulas giving all the solutions to
7x + 11y = 100
where x and y are integers.
Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2
I am exactly n times my daughter's age. In m years I shall be ... How old am I?
How can we solve equations like 13x + 29y = 42 or 2x +4y = 13 with
the solutions x and y being integers? Read this article to find
Find the maximum value of 1/p + 1/q + 1/r where this sum is less than 1 and p, q, and r are positive integers.
The symbol [ ] means 'the integer part of'. Can the numbers [2x];
2[x]; [x + 1/2] + [x - 1/2] ever be equal? Can they ever take three
The first of five articles concentrating on whole number dynamics, ideas of general dynamical systems are introduced and seen in concrete cases.
Let a(n) be the number of ways of expressing the integer n as an
ordered sum of 1's and 2's. Let b(n) be the number of ways of
expressing n as an ordered sum of integers greater than 1. (i)
Calculate. . . .
Show that if you add 1 to the product of four consecutive numbers
the answer is ALWAYS a perfect square.
Investigate the sequences obtained by starting with any positive 2
digit number (10a+b) and repeatedly using the rule 10a+b maps to
10b-a to get the next number in the sequence.
Start with any whole number N, write N as a multiple of 10 plus a remainder R and produce a new whole number N'. Repeat. What happens?
If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.
Can you explain why a sequence of operations always gives you perfect squares?
A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?
To make 11 kilograms of this blend of coffee costs £15 per
kilogram. The blend uses more Brazilian, Kenyan and Mocha coffee...
How many kilograms of each type of coffee are used?
Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...
Ranging from kindergarten mathematics to the fringe of research
this informal article paints the big picture of number in a non
technical way suitable for primary teachers and older students.
Explore the properties of some groups such as: The set of all real
numbers excluding -1 together with the operation x*y = xy + x + y.
Find the identity and the inverse of the element x.
Find a condition which determines whether the hyperbola y^2 - x^2 =
k contains any points with integer coordinates.
Using the 8 dominoes make a square where each of the columns and rows adds up to 8
Explore the factors of the numbers which are written as 10101 in
different number bases. Prove that the numbers 10201, 11011 and
10101 are composite in any base.
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?
Why are there only a few lattice points on a hyperbola and
infinitely many on a parabola?