This problem of Waring's is unsolved: For all $n \ge 2 $, $\lfloor (\frac 32 ) ^n \rfloor + {3^n} \bmod{2^n} < 2^n $. (Kubina and Wunderlich have tested this up to $471,600,000$.) This can be converted into a "C-like" program:
x = 9; y = 4; while ( x/y + x%y < y ) { x = 3*x; y = 2*y; }
which can be shortened slightly to:
x = 9; for( y = 4 ; x/y + x%y < y ; y *= 2 ) x *= 3;
Does anyone know of an unsolved problem which can be converted into a shorter program? The program must halt iff the problem is false. Put differently, I conjecture that the above program is the shortest whose halting is unknown. I want the program to be C-like, with integers of unlimited size.