Diophantine equations

problem

BT... Eat Your Heart Out

Age

16 to 18

Challenge level

2 out of 3

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?
problem

Exhaustion

Age

16 to 18

Challenge level

2 out of 3

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2
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Euclid's Algorithm I

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.
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Euclid's Algorithm II

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.