4. Find all functions f: Z→Z, such that for all a+b+c = 0 holds :
f(a)^2 + f(b)^2 + f(c)^2 = 2f(a)f(b) + 2f(b)f(c) + 2f(c)f(a)
5. Let △ABC be a triangle with ∠C = 90度 and that D be the foot of the
altitude from C. Let X be a point in the interior of the segment CD.
Let K be the point on the segment AX such that BK = BC. Similarly,
let L be the point on the segment BX such that AL = AC.
Let M be the point of intersection of AL and BK.
Show that MK = ML.
6. Determine all positive integers n for which there exist non-negative
integers a_1, a_2, ...,a_n such that:
1 1 1 1 2 n