URM program to compute n^m (n to the power of m)
For n≠0 and m≠0,
1 S(6)
2 S(7)
3 C(1,3)
4 C(1,4)
5 J(2,7,19)
6 J(4,6,14)
7 J(3,5,11)
8 S(1)
9 S(5)
10 J(1,1,7)
11 S(6)
12 Z(5)
13 J(1,1,6)
14 C(1,3)
15 S(7)
16 Z(6)
17 S(6)
18 J(1,1,5)
n | m | 0 | 0 | 0 | 0 | 0 |
n | m | n | n | 0 | 1 | 1 |
n+1 | m | n | n | 1 | 1 | 1 |
n+2 | m | n | n | 2 | 1 | 1 |
n+3 | m | n | n | 3 | 1 | 1 |
… | … | … | … | … | … | … |
n+n=2n | m | n | n | n | 1 | 1 |
2n | m | n | n | 0 | 2 | 1 |
2n+1 | m | n | n | 1 | 2 | 1 |
2n+2 | m | n | n | 2 | 2 | 1 |
… | … | … | … | … | … | … |
2n+n=3n | m | n | n | n | 2 | 1 |
3n | m | n | n | 0 | 3 | 1 |
… | … | … | … | … | … | … |
… | … | … | … | … | … | … |
n(n)=n2 | m | n | n | n | n-1 | 1 |
n2 | m | n | n | 0 | n | 1 |
n2 | m | n2 | n | 0 | 1 | 2 |
n2+1 | m | n2 | n | 1 | 1 | 2 |
n2+2 | m | n2 | n | 2 | 1 | 2 |
… | … | … | … | … | … | … |
n2+n2=2n2 | m | n2 | n | n2 | 1 | 2 |
2n2 | m | n2 | n | 0 | 2 | 2 |
… | … | … | … | … | … | … |
… | … | … | … | … | … | … |
n(n2)=n3 | m | n2 | n | n2 | n | 2 |
n3 | m | n2 | n | 0 | n | 2 |
n3 | m | n3 | n | 0 | 1 | 3 |
… | … | … | … | … | … | … |
… | … | … | … | … | … | … |
… | … | … | … | … | … | … |
n(nm-1)=nm | m | nm-1 | n | nm-1 | n | m-1 |
nm | m | nm | n | 0 | 1 | m |
Example 1.
2 | 4 | 0 | 0 | 0 | 0 | 0 |
2 | 4 | 2 | 2 | 0 | 1 | 1 |
3 | 4 | 2 | 2 | 1 | 1 | 1 |
4 | 4 | 2 | 2 | 2 | 1 | 1 |
4 | 4 | 2 | 2 | 0 | 2 | 1 |
4 | 4 | 4 | 2 | 0 | 1 | 2 |
5 | 4 | 4 | 2 | 1 | 1 | 2 |
6 | 4 | 4 | 2 | 2 | 1 | 2 |
7 | 4 | 4 | 2 | 3 | 1 | 2 |
8 | 4 | 4 | 2 | 4 | 1 | 2 |
8 | 4 | 4 | 2 | 0 | 2 | 2 |
8 | 4 | 8 | 2 | 0 | 1 | 3 |
9 | 4 | 8 | 2 | 1 | 1 | 3 |
10 | 4 | 8 | 2 | 2 | 1 | 3 |
11 | 4 | 8 | 2 | 3 | 1 | 3 |
12 | 4 | 8 | 2 | 4 | 1 | 3 |
13 | 4 | 8 | 2 | 5 | 1 | 3 |
14 | 4 | 8 | 2 | 6 | 1 | 3 |
15 | 4 | 8 | 2 | 7 | 1 | 3 |
16 | 4 | 8 | 2 | 8 | 1 | 3 |
16 | 4 | 8 | 2 | 0 | 2 | 3 |
16 | 4 | 16 | 2 | 0 | 1 | 4 |
Example 2.
3 | 3 | 0 | 0 | 0 | 0 | 0 |
3 | 3 | 3 | 3 | 0 | 1 | 1 |
4 | 3 | 3 | 3 | 1 | 1 | 1 |
5 | 3 | 3 | 3 | 2 | 1 | 1 |
6 | 3 | 3 | 3 | 3 | 1 | 1 |
6 | 3 | 3 | 3 | 3 | 2 | 1 |
6 | 3 | 3 | 3 | 0 | 2 | 1 |
7 | 3 | 3 | 3 | 1 | 2 | 1 |
8 | 3 | 3 | 3 | 2 | 2 | 1 |
9 | 3 | 3 | 3 | 3 | 2 | 1 |
9 | 3 | 3 | 3 | 3 | 2 | 1 |
9 | 3 | 3 | 3 | 0 | 3 | 1 |
9 | 3 | 9 | 3 | 0 | 1 | 2 |
10 | 3 | 9 | 3 | 1 | 1 | 2 |
11 | 3 | 9 | 3 | 2 | 1 | 2 |
12 | 3 | 9 | 3 | 3 | 1 | 2 |
13 | 3 | 9 | 3 | 4 | 1 | 2 |
14 | 3 | 9 | 3 | 5 | 1 | 2 |
15 | 3 | 9 | 3 | 6 | 1 | 2 |
16 | 3 | 9 | 3 | 7 | 1 | 2 |
17 | 3 | 9 | 3 | 8 | 1 | 2 |
18 | 3 | 9 | 3 | 0 | 2 | 2 |
19 | 3 | 9 | 3 | 1 | 2 | 2 |
20 | 3 | 9 | 3 | 2 | 2 | 2 |
21 | 3 | 9 | 3 | 3 | 2 | 2 |
22 | 3 | 9 | 3 | 4 | 2 | 2 |
23 | 3 | 9 | 3 | 5 | 2 | 2 |
24 | 3 | 9 | 3 | 6 | 2 | 2 |
25 | 3 | 9 | 3 | 7 | 2 | 2 |
26 | 3 | 9 | 3 | 8 | 2 | 2 |
27 | 3 | 9 | 3 | 9 | 2 | 2 |
27 | 3 | 9 | 3 | 0 | 3 | 2 |
27 | 3 | 27 | 3 | 0 | 1 | 3 |
For any positive integers n and m,
1 J(1,3,3)
2 J(2,3,23)
3 J(2,3,22)
4 S(6)
5 S(7)
6 C(1,3)
7 C(1,4)
8 J(2,7,25)
9 J(4,6,17)
10 J(3,5,14)
11 S(1)
12 S(5)
13 J(1,1,10)
14 S(6)
15 Z(5)
16 J(1,1,9)
17 C(1,3)
18 S(7)
19 Z(6)
20 S(6)
21 J(1,1,8)
22 J(1,1,22)
23 Z(1)
24 S(1)
Note: if n=m=0, the answer is undetermined and the program never stops.