OFFSET
0,2
COMMENTS
From the riddle on the tombstone of Diophantus. See the reference and the links.
REFERENCES
H.-W. Alten et al., 4000 Jahre Algebra, 2. Auflage, Springer, 2014, p. 63.
LINKS
David Pleacher, Diophantus' epitaph.
Eric Weisstein's World of Mathematics, Diophantus's Riddle.
Wikipedia, Diophantus.
FORMULA
a(0): birth (all numbers a(n) in years), a(1): boyhood ended, a(2): beard started to grow, a(3): marriage, a(4): birth of son, a(5): death of son, a(6): death of Diophantus.
EXAMPLE
a(1) = age/6,
a(2) = age*(1/6 + 1/12) = age/4,
a(3) = age*(1/4 + 1/7) = age*11/28,
a(4) = age*11/28 + 5,
a(5) = age(11/28 + 1/2) + 5 = age*25/28 + 5,
a(6) = age*25/28 + 5 + 4 = age,
hence age*(1-25/28) = 9, age = 28*3 = 84.
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Wolfdieter Lang, Jan 31 2015
STATUS
approved