Is there a convex quadrilateral, whose diagonals divide it into four triangles, such that their areas are four distinct prime integers.
No. Let the areas of those triangles be the prime numbers \( p, q, r \) and \( t \). But for the areas of the triangles we have \( pq = rt \), where the triangles with areas \( p \) and \( q \) have only a common vertex. This is not possible for distinct primes.