There are 24 NRICH Mathematical resources connected to Diophantine equations, you may find related items under Algebraic expressions, equations and formulae.
Broad Topics > Algebraic expressions, equations and formulae > Diophantine equations
If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.
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 each price?
The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?
Why are there only a few lattice points on a hyperbola and infinitely many on a parabola?
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.
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.
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.
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?
Find integer solutions to: $\sqrt{a+b\sqrt{x}} + \sqrt{c+d.\sqrt{x}}=1$
According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?
Can you find formulas giving all the solutions to 7x + 11y = 100 where x and y are integers?
Can you work out how many of each kind of pencil this student bought?
When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...
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?
What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?
Try out this geometry problem involving trigonometry and number theory
I am exactly n times my daughter's age. In m years I shall be ... How old am I?
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.
Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2
The sum of the cubes of two numbers is 7163. What are these numbers?
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?
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?
Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2
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?