- Show that there is a total computable function
*k*such that for each*n*,*k*(*n*) is an index of the function . - Show that there is a total computable function
*k*such that for each*n*, the set of perfect powers. - Let . Show that there is a total computable function
*s*such that - Show that the functions defined in the proof of the
*s*-*m*-*n*theorem are primitive recursive. - Show that for each
*m*there is a total (*m*+1)-ary computable function such that for all*n*where and are

*m*- and*n*-tuples respectively.

Sat Sep 27 16:37:46 IST 1997