for 17

f(10,000,000,001) = 10,000,000,001 <wrong

Arrgh off by 1

f(9,999,999,990) = 9,999,999,999
f(9,999,999,999) = 10,000,000,000
f(10,000,000,000) = 10,000,000,001
f(10,000,000,001) = 10,000,000,002
f(10,000,000,002) = 10,000,000,002 < right

For 16

Assume an equalatral triangle. (The test said I could)
bisect each of two sides to determine the midpoint.
draw a line from each midpoint to the opposite vertex.
where they cross is P.
And the specified triangles have the same perimeters.