Is Diophantus and his son old?

If you don’t know the story:

His youth lasted 1/6 of his life. He grew a beard 1/12 of his life later. After 1/7 more of his life, he got married, and five years later, his son was introduced to the world. Diophantus’s son lived half his father’s life, and Diophantus died four years after his son. How long did Diophantus live?

Let D be Diophantus’s age when he died. Let S be his son’s age when he died. D/6 + D/12 + D/7 + 5 + S + 4 = S: 33D/84 + 9 + 42D/84 = 75D/84 + 9: 9D/84 = 9: D=84, S=42.

Does this do anything? Yes.

Diophantine equations.

Were they old? Surely, the son died way too early, right? WRONG!

Probably died to leukaemia or suffocation or suicide.


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