Diophantine equation
Typical problem

The given information is that a father's age is 1 less than twice that of his son, and that the digits AB making up the father's age are reversed in the son's age (i.e. BA). This leads to the equation 10 A + B = 2(10 B + A) − 1, thus 19 B − 8 A = 1. Inspection gives the result A = 7, B = 3, and thus AB equals 73 years and BA equals 37 years. One may easily show that there is not any other solution with A and B positive integers less than 10.

Many well known puzzles in the field of recreational mathematics lead to diophantine equations. Examples include the cannonball problem, Archimedes's cattle problem and the monkey and the coconuts.
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