cp's OEIS Frontend

A200505 Least m>0 such that n = 5^x-y^2 (mod m) has no solution, or 0 if no such m exists.

%I A200505 #16 Mar 31 2012 13:48:35
%S A200505 0,0,4,4,0,0,4,4,5,0,4,4,24,5,4,4,0,15,4,4,75,0,4,4,0,0,4,4,5,39,4,4,
%T A200505 15,5,4,4,24,35,4,4,175,31,4,4,0,39,4,4,5,0,4,4,35,5,4,4,21,55,4,4,24,
%U A200505 0,4,4,31,39,4,4,5,399,4,4,31,5,4,4,0,15,4,4
%N A200505 Least m>0 such that n = 5^x-y^2 (mod m) has no solution, or 0 if no such m exists.
%C A200505 If such an m>0 exists, this proves that n is not in A051216, i.e., not of the form 5^x-y^2. On the other hand, if there are integers x, y such that n=5^x-y^2, then we know that a(n)=0.
%C A200505 a(144) > 20000.
%H A200505 M. F. Hasler, <a href="/A200505/b200505.txt">Table of n, a(n) for n = 0..143</a>
%F A200505 a(2+4k)=a(3+4k)=4, a(8+20k)=a(13+20k)=5 for all k>=0.
%e A200505 See A200507.
%o A200505 (PARI) A200505(n,b=5,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,i,i^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 A200505 Cf. A051204-A051221, A200505-A200524.
%K A200505 nonn
%O A200505 0,3
%A A200505 _M. F. Hasler_, Nov 18 2011