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PROG
| (PARI) { f(a, b) = (a+1)*(a-1)*(b+1)*(b-1) } ans=vector(6, x, [0, 0]); clear=ans; { g(a) = b=divisors(a*a-1); l=length(b); b=b+vector(l, x, a); for(x=1, l/2, c=4*a*b[x]*(a+1)*(a-1)*(b[x]+1)*(b[x]-1)*(a*b[x]-1)/((b[x]-a)*(b[x]-a));
d=floor(sqrt(sqrt(c))); count=1; for( y=2, d, if (c%(y*y-1)==0, e=ceil(sqrt(c/(y*y-1))); if (f(y, e)==c, ans[count]=[y, e]; count=count+1, ), ); ); if ( count>5, print("g:", a, " ", c, " ", ans); ans=clear, ); ); } { find()= for(n=560, 10001, print(n); g(n)); }
Store program as text file, load gp, \r textfilename and then run function find() to search for a 7th entry.
(PARI) { f(a, b) = (a+1)*(a-1)*(b+1)*(b-1) } ans=vector(6, x, [0, 0])
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