### There are 17 results

Broad Topics >

Algebra > Diophantine equations

##### Age 16 to 18 Challenge Level:

The familiar Pythagorean 3-4-5 triple gives one solution to (x-1)^n
+ x^n = (x+1)^n so what about other solutions for x an integer and
n= 2, 3, 4 or 5?

##### Age 16 to 18

We continue the discussion given in Euclid's Algorithm I, and here we shall discover when an equation of the form ax+by=c has no solutions, and when it has infinitely many solutions.

##### Age 14 to 16 Challenge Level:

All CD Heaven stores were given the same number of a popular CD to
sell for £24. In their two week sale each store reduces the
price of the CD by 25% ... How many CDs did the store sell at. . . .

##### Age 16 to 18 Challenge Level:

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

##### Age 14 to 16 Challenge Level:

I am exactly n times my daughter's age. In m years I shall be ... How old am I?

##### Age 14 to 16 Challenge Level:

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?

##### Age 16 to 18 Challenge Level:

If the last four digits of my phone number are placed in front of the remaining three you get one more than twice my number! What is it?

##### Age 16 to 18 Challenge Level:

Find all 3 digit numbers such that by adding the first digit, the
square of the second and the cube of the third you get the original
number, for example 1 + 3^2 + 5^3 = 135.

##### Age 16 to 18

Beautiful mathematics. Two 18 year old students gave eight
different proofs of one result then generalised it from the 3 by 1
case to the n by 1 case and proved the general result.

##### Age 14 to 16 Challenge Level:

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?

##### Age 14 to 18 Challenge Level:

Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2

##### Age 14 to 16 Challenge Level:

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.

##### Age 14 to 16 Challenge Level:

Find integer solutions to: $\sqrt{a+b\sqrt{x}} + \sqrt{c+d.\sqrt{x}}=1$

##### Age 16 to 18

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
out.

##### Age 14 to 18 Challenge Level:

A java applet that takes you through the steps needed to solve a
Diophantine equation of the form Px+Qy=1 using Euclid's algorithm.

##### Age 16 to 18 Challenge Level:

Try out this geometry problem involving trigonometry and number theory

##### Age 14 to 16 Challenge Level:

If the altitude of an isosceles triangle is 8 units and the perimeter of the triangle is 32 units.... What is the area of the triangle?