# Search by Topic

#### Resources tagged with Diophantine equations similar to Code to Zero:

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Stage:
Challenge level:

### There are 17 results

Broad Topics > Algebra > Diophantine equations

### Code to Zero

##### Stage: 5 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.

### Shades of Fermat's Last Theorem

##### Stage: 5 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?

### Exhaustion

##### Stage: 5 Challenge Level:

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

### BT.. Eat Your Heart Out

##### Stage: 5 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?

### CD Heaven

##### Stage: 4 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. . . .

### Euclid's Algorithm II

##### Stage: 5

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.

### Double Angle Triples

##### Stage: 5 Challenge Level:

Try out this geometry problem involving trigonometry and number theory

### Our Ages

##### Stage: 4 Challenge Level:

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

### Coffee

##### Stage: 4 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?

### Rudolff's Problem

##### Stage: 4 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?

### Are You Kidding

##### Stage: 4 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?

### In Particular

##### Stage: 4 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.

### Why Stop at Three by One

##### Stage: 5

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.

### Upsetting Pitagoras

##### Stage: 4 and 5 Challenge Level:

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

### Deep Roots

##### Stage: 4 Challenge Level:

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

### Solving with Euclid's Algorithm

##### Stage: 4 and 5 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.

### Euclid's Algorithm I

##### Stage: 5

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.
The text passage is a collection of mathematical problems and questions, primarily focused on Diophantine equations, which are equations that require integer solutions. Each problem is presented as a separate challenge with varying levels of complexity.
multiple_questions

the passage contains multiple distinct mathematical questions or problems, but does not provide answers to these questions. each problem is a separate diophantine equation or related challenge, such as finding integer solutions to specific equations or solving geometric problems with integer constraints.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Search by Topic

#### Resources tagged with Diophantine equations similar to Code to Zero:

Filter by: Content type:
Stage:
Challenge level:

### There are 17 results

Broad Topics > Algebra > Diophantine equations

### Code to Zero

##### Stage: 5 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.

### Shades of Fermat's Last Theorem

##### Stage: 5 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?

### Exhaustion

##### Stage: 5 Challenge Level:

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

### BT.. Eat Your Heart Out

##### Stage: 5 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?

### CD Heaven

##### Stage: 4 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. . . .

### Euclid's Algorithm II

##### Stage: 5

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.

### Double Angle Triples

##### Stage: 5 Challenge Level:

Try out this geometry problem involving trigonometry and number theory

### Our Ages

##### Stage: 4 Challenge Level:

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

### Coffee

##### Stage: 4 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?

### Rudolff's Problem

##### Stage: 4 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?

### Are You Kidding

##### Stage: 4 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?

### In Particular

##### Stage: 4 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.

### Why Stop at Three by One

##### Stage: 5

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.

### Upsetting Pitagoras

##### Stage: 4 and 5 Challenge Level:

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

### Deep Roots

##### Stage: 4 Challenge Level:

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

### Solving with Euclid's Algorithm

##### Stage: 4 and 5 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.

### Euclid's Algorithm I

##### Stage: 5

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.
user
The text passage is a collection of mathematical problems and questions, primarily focused on Diophantine equations, which are equations that require integer solutions. Each problem is presented as a separate challenge with varying levels of complexity.

TYPE: MULTIPLE_QUESTIONS

The passage contains multiple distinct mathematical questions or problems, but does not provide answers to these questions. Each problem is a separate Diophantine equation or related challenge, such as finding integer solutions to specific equations or solving geometric problems with integer constraints.