##
Birthday Triangles

It's my birthday, and I tried to find a puzzle related to it. I was
hoping to find that my birth year and the current year (1998) could
both be used as two sides of a Pythagorean Triangle
(a right triangle with integral sides), but
that was not to be.
But luckily, I was able to determine that there will come one (and only one)
year when my birth year and the current year are two of the sides of such a
triangle (I'll be an even age, as I am now, but I'll not yet be 100 years old.)
- How old am I today? (I'm not 22.)
- What birth year this century can be used in the greatest number of
such birthday triangles? (Where the birth year and a greater year within
100 years are both sides of a Pythagorean Triangle.)
- What birth year next century?

Source: Original.

Solution

Mail to Ken