Diophantine equations

There are 25 NRICH Mathematical resources connected to Diophantine equations
BT.. Eat your heart out
problem

Bt.. eat your heart out

Age
16 to 18
Challenge level
filled star filled star empty star
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?
Are you kidding
problem

Are you kidding

Age
14 to 16
Challenge level
filled star filled star empty star
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?
Why stop at Three by One
article

Why stop at three by one

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.
Euclid's Algorithm I
article

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.
Euclid's Algorithm II
article

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.