19/2/07

Diophantus




Diophantus was a Greek mathematician sometimes known as 'the father of algebra' who is best known for his Arithmetica. This had an enormous influence on the development of number theory.



Diophantus introduced symbols for subtraction, for an unknown, and for the degree of the variable. Although there were several solutions to some of his problems, he only looked for one positive integer solution. Now we call an equation to be solved in integers a diophantine equation. For example, Diophantus considered the equations
ax + by = c where the variables x and y are positive integers.

"Here lies Diophantus," the wonder behold . . .

Through art algebraic, the stone tells how old:

"God gave him his boyhood one-sixth of his life,

One twelfth more as youth while whiskers grew rife;

And then yet one-seventh ere marriage begun;

In five years there came a bouncing new son.

Alas, the dear child of master and sage

After attaining half the measure of his fathers lifechill fate took him.

After consoling his fate by this science of numbers for four years, he ended his life."


Find Diophantus' age at death.



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