The Mathematics of PE

Let us have a short look at the mathematics of P_E. It uses the set of functions A_a(n)

A_a(n) = (a-2n)n² = an² - 2n³

One readily sees that

A₁₇(5) = 175
A₁₇(6) = 180
A₁₇(7) = 147

are the ages of Avraham, Yitzchak, and Ya'akov. The implied age is

A₁₇(4) = 144

and is the only one left that is over 100. The ages

A₁₇(8) = 64
A₁₇(3) = 99

will be explained later. The maximum age is reached when

2an - 6n² = 0

which is at n = a/3, for continuous n, and the maximum reaches the value

A_a(a/3) = (a/3)³

For a=17, the value a/3 is closest to 6, and therefore Yitzchak reaches the oldest age.