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## Homework Statement

This is not homework but I am trying to solve a problem to see to general a set of numbers for the grassmanian equations to use in something else.[/B]

**I have five variables a,b,c,d,e. a-b,a-c,a-d,a-e,b-a,b-c,.....etc so that none of them are the same so it generates all numbers from 1,2,3,4,....20 in modular 21. Clearly a,b,c,d,e can not be the same since it will obviously not generate all the numbers. Below is my matlab code.**

**a,b,c,d,e must be in the {0,1,2,3,....20}**

**The code does not even output anything.**

## The Attempt at a Solution

Matlab:

```
clear all;
close all;
k=21;
flag =0;
for i =0:16
a=i;
if flag ==1
break;
end
for j=1:17
b=j;
if flag == 1
break;
end
for h =2:18
c= h;
if flag == 1
break;
end
for l=3:19
d=l;
if flag ==1
break;
end
for p=4:20
e=p;
g1=a-b;
g2=a-c;
g3=a-d;
g4=a-e;
g5=b-a;
g6=b-c;
g7=b-d;
g8=b-e;
g9=c-a;
g10=c-b;
g11=c-d;
g12=c-e;
g13=d-a;
g14=d-b;
g15=d-c;
g16=d-e;
g17=e-a;
g18=e-b;
g19=e-c;
g20=e-d;
G=[ mod(g1,k), mod(g2,k), mod(g3,k), mod(g4,k), mod(g5,k), mod(g6,k), mod(g7,k), mod(g8,k), mod(g9,k), mod(g10,k), mod(g11,k), mod(g12,k), mod(g13,k), mod(g14,k), mod(g15,k), mod(g16,k), mod(g17,k), mod(g18,k), mod(g19,k), mod(g20,k)];
S=sort(G);
AllElements=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20];
true=isequal(S,AllElements);
if (true == 1)
answers=[a,b,c,d,e];
flag = 1;
break;
end
end
end
end
end
end
```

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