# Resources tagged with: Diophantine equations

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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 ### Letter Land

##### Age 11 to 14Challenge Level

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. ### CD Heaven

##### Age 14 to 16Challenge 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. . . . ### Fibs

##### Age 11 to 14Challenge Level

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? ### Lattice Points

##### Age 16 to 18Challenge Level

Why are there only a few lattice points on a hyperbola and infinitely many on a parabola? ### Euclid's Algorithm II

##### 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. ### Euclid's Algorithm I

##### 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. ### Why Stop at Three by One

##### 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. ### Are You Kidding

##### Age 14 to 16Challenge 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? ### Deep Roots

##### Age 14 to 16Challenge Level

Find integer solutions to: $\sqrt{a+b\sqrt{x}} + \sqrt{c+d.\sqrt{x}}=1$ ### Plutarch's Boxes

##### Age 11 to 14Challenge Level

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. . . . ### In Particular

##### Age 14 to 16Challenge Level

Can you find formulas giving all the solutions to 7x + 11y = 100 where x and y are integers? ### Whole Numbers Only

##### Age 11 to 14 ShortChallenge Level

Can you work out how many of each kind of pencil this student bought? ### Not a Polite Question

##### Age 11 to 14 ShortChallenge Level

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... ### Coffee

##### Age 14 to 16Challenge 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? ### Hallway Borders

##### Age 11 to 14Challenge Level

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? ### Double Angle Triples

##### Age 16 to 18Challenge Level

Try out this geometry problem involving trigonometry and number theory ### Our Ages

##### Age 14 to 16Challenge Level

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

##### Age 16 to 18Challenge 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. ### Exhaustion

##### Age 16 to 18Challenge Level

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

##### Age 16 to 18Challenge Level

The sum of the cubes of two numbers is 7163. What are these numbers? ### BT.. Eat Your Heart Out

##### Age 16 to 18Challenge 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? ### Rudolff's Problem

##### Age 14 to 16Challenge Level

A group of 20 people pay a total of Â£20 to see an exhibition. The admission price is Â£3 for men, Â£2 for women and 50p for children. How many men, women and children are there in the group? ### Upsetting Pitagoras

##### Age 14 to 18Challenge Level

Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2 ### Shades of Fermat's Last Theorem

##### Age 16 to 18Challenge 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?