For J and L (J<L) I want to find that values of p and q which satisfies mod(((i^b-​i^a)*(i^d-​i^c)),j)~=​0 for all values of 0<=a<b<=J-1 and 0<=c<d<=L-1. If mod(((i^b-​i^a)*(i^d-​i^c)),j)==​0 at any stage we break the loop and go for next values of p and q

J=input('Value of J: ');
L=input('Value of L: ');
for j = L:6;
    for i = 2:j-1;
        for a=0:J-1;
            for b=a+1:J-1;
                for c = 0:L-1;
                    for d = c+1:L-1;
                        if mod(((i^b-i^a)*(i^d-i^c)),j)~=0
                           p_q=[i,j]
                        end
                    end
                end
            end
        end
    end
end

output:

p_q = 2 3

p_q = 2 3

p_q = 2 4

p_q = 2 4

p_q = 2 4

p_q = 2 5

p_q = 2 5

p_q = 2 5

p_q = 3 5

p_q = 3 5

p_q = 3 5

p_q = 4 5

p_q = 4 5

p_q = 2 6

and so on.

Here the required answer is p=2 and q=5; it is the only combination for which mod(((i^b-i^a)*(i^d-i^c)),j)~=0 for any values of a,b,c,d. But here it is showing so many answers. Kindly help me.

[Matt J]

What values for J and L did you test here?

[Jasvinder Singh]

Initially I am checking for J=2 and L=3

Answer 1

[Matt J]

[a,b,c,d]=ndgrid(0:J-1,0:J-1,  0:L-1, 0:L-1);
  k=a<b & c<d;
  
[a,b,c,d]=deal( a(k),  b(k), c(k), d(k)); %all allowed combinations
p_q=cell(6,6);

for j = L:6
    for i = 2:j-1
        
        if   all( mod( (i.^b-i.^a).*(i.^d-i.^c) ,j)  )
         
          p_q{i,j} =[i,j];

        end
         
    end
end

p_q=vertcat(p_q{:})

[Jasvinder Singh]

sir, it seems much better than mine but still it is not working. for example for J=2, L=3, p and q cannot be 2 and 4 respectively becaure for a=0, b=1, c=2 and d=3;

mod( (i^b-i^a)*(i^d-i^c),j)) is zero and so we not need these p and q.

Thanks

[Matt J]

But d cannot equal 3 when L=3. In your original post, you say that 0<=d<=L-1, so the maximum value d can assume is 2.

[Jasvinder Singh]

Yes, sir it was actually [a,b,c,d]=ndgrid(0:J,0:J, 0:L, 0:L);

It is working now.

Thank you so much sir