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For J and L (J<L) I want to find that values of p and q which satisfy all the 7 conditions (mention in code) for each 0<=a<b<c<=J and 0<=d<e<f<=L

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Jasvinder Singh
Jasvinder Singh 2019-6-6
关闭： MATLAB Answer Bot 2021-8-20
J=input('J: ');
L=input('L: ');
[a,b,c,d]=ndgrid(1:J,1:J, 1:L, 1:L);
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:3*L
for i = 2:j-1
k = all( mod( (i.^b-i.^a).*(i.^d-i.^c) ,j) )
p_q{i,j} =[i(k), j(k)]
end
end
p_q=vertcat(p_q{:})
The above code is working for single equation but now the condtion is differrent. Here, we have 0<a<b<c<=J, 0<d<e<f<=L;
j=L : uptil the required value is not found
i=2 : j-1
and the conditions are:
for the first equation we have to check for only 0<a<b<=J, 0<d<=L.
mod( (i.^b-i.^a).*(i.^d-i.^c) ,j)
but for the remaining 6 conditions we have to check for 0<a<b<c<=J, 0<d<e<f<=L
and the conditions are
  1. mod(((i.^d).*(i.^a-i.^c)+(i.^e).*(i.^c-i.^b)+(i.^f).*(i.^b-i.^a)),j )~=0
  2. mod(((i.^d).*(i.^a-i.^c)+(i.^f).*(i.^c-i.^b)+(i.^e).*(i.^b-i.^a)),j )~=0
  3. mod(((i.^d).*(i.^b-i.^c)+(i.^f).*(i.^c-i.^a)+(i.^e).*(i.^a-i.^b)),j )~=0
  4. mod(((i.^d).*(i.^a-i.^b)+(i.^e).*(i.^b-i.^c)+(i.^f).*(i.^c-i.^a)),j )~=0
  5. mod(((i.^d).*(i.^a-i.^b)+(i.^f).*(i.^b-i.^c)+(i.^e).*(i.^c-i.^a)),j )~=0
  6. mod(((i.^d).*(i.^b-i.^c)+(i.^e).*(i.^c-i.^a)+(i.^f).*(i.^a-i.^b)),j )~=0
for example
for J=3 and L=4 if we take p=2 q=9 then 6th condition is not satisfied for a=1 b=2 c=3 and d=2 ,e=2, f=3 so we cannot select these values of p and q
next we take p=3 and q=9 then all conditions are not satisfies again we go to next one
on contiuing in this way we will check for all values of p=2 to 9 for q=9 but all the combinaitons are rejected.
and then we will check for q=10, 11, ....... and so on uptil we get the required values of p and q.
Kindly help me in this matter.

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