Monday, 25 March 2013

MONDAY, 25 MARCH 2013

Today is the $84^{th}$ day of the year.

$84 = 2^2 \times 3 \times 7$

$84$ is a member of the following primitive Pythagorean triples:
$(13, 84, 85)$
$(187, 84, 205)$
$(437, 84, 445)$
$(1763, 84, 1765)$

$1^2 + 3^2 + 5^2 + 7^2 = 1 + 9 + 25 + 49 = 84$ making $84$ a member of the sequence $\sum_{k=1}^n (2n-1)^2 = \frac {n(2n - 1)(2n + 1)}{3}$ which is the sum of the odd numbers squared, see A000447.