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

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Jasvinder Singh 2019-6-5

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/465610-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

评论： Jasvinder Singh 2019-6-5

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 4

p_q = 2 5

p_q = 3 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.

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Matt J 2019-6-5

What values for J and L did you test here?

Jasvinder Singh 2019-6-5

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

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Answer 1

Matt J 2019-6-5

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/465610-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#answer_377950

编辑：Matt J 2019-6-5

在 MATLAB Online 中打开

[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{:})