0,1

K. S. Brown, Numbers Expressible as (a^2-1)(b^2-1)

K. S. Brown, MathPages Most Wanted List, Problem #14.

(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/PARI, \r textfilename and then run function find() to search for a 7th entry.

(GP/PARI) { f(a, b) = (a+1)*(a-1)*(b+1)*(b-1) } ans=vector(6, x, [0, 0])

Cf. A063066, A063067, A063068.

Sequence in context: A090468 A071135 A032755 this_sequence A134858 A145277 A123705

Adjacent sequences: A057532 A057533 A057534 this_sequence A057536 A057537 A057538

nonn

K. S. Brown (ksbrown(AT)seanet.com), Fred W. Helenius (fredh(AT)ix.netcom.com), Dean Hickerson (dean.hickerson(AT)yahoo.com), Randall L. Rathbun