Editing Diophantine equation (section)

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