cp's OEIS Frontend

A200518 Least m>0 such that n = y^2-8^x (mod m) has no solution, or 0 if no such m exists.

%I A200518 #9 Mar 31 2012 13:48:35
%S A200518 0,0,4,0,7,7,4,9,0,7,4,7,7,8,4,0,7,0,4,7,32,8,4,7,0,7,4,16,0,8,4,9,7,
%T A200518 7,4,0,0,7,4,7,7,0,4,9,7,8,4,7,0,9,4,7,9,7,4,12,0,0,4,16,7,7,4,0,0,7,
%U A200518 4,7,7,8,4,16,7,0,4,7,9,8,4,7,0,7,4,32
%N A200518 Least m>0 such that n = y^2-8^x (mod m) has no solution, or 0 if no such m exists.
%C A200518 If a(n)>0, this proves that n cannot be a member of A051210, i.e., cannot be written as y^2-8^x. To prove that an integer n is in A051210, it is sufficient to find integers x,y such that y^2-8^x=n. In that case, a(n)=0.
%H A200518 M. F. Hasler, <a href="/A200518/b200518.txt">Table of n, a(n) for n = 0..1000</a>
%e A200518 See A200512 for motivation and detailed examples.
%o A200518 (PARI) A200518(n,b=8,p=3)={ my( x=0, qr, bx, seen ); for( m=3,9e9, while( x^p < m, issquare(b^x+n) & return(0); x++); qr=vecsort(vector(m,y,y^2-n)%m,,8); seen=0; bx=1; until( bittest(seen+=1<<bx, bx=bx*b%m), for(i=1,#qr, qr[i]<bx & next; qr[i]>bx & break; next(3))); return(m))}
%Y A200518 Cf. A051204-A051221, A200505-A200520.
%K A200518 nonn
%O A200518 0,3
%A A200518 _M. F. Hasler_, Nov 18 2011