text: # Search by Topic
  
  #### Resources tagged with Diophantine equations similar to Code to Zero:
  
  Filter by: Content type:
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  ### 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.
explanation: The document is a collection of math problems, specifically Diophantine equations, which are equations that require integer solutions. Each problem is presented with a brief description and a challenge level. The document does not contain answers to the questions, only the questions themselves.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # 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.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a collection of math problems, specifically Diophantine equations, which are equations that require integer solutions. Each problem is presented with a brief description and a challenge level. The document does not contain answers to the questions, only the questions themselves.
  
  Label: multiple-question