

A200523


Least m>0 such that n = 3^xy^2 (mod m) has no solution, or 0 if no such m exists.


4



0, 0, 0, 0, 8, 0, 8, 9, 0, 0, 12, 0, 8, 9, 8, 20, 9, 0, 0, 12, 8, 80, 8, 0, 45, 9, 0, 0, 8, 80, 8, 9, 0, 45, 9, 20, 8, 21, 8, 80, 9, 80, 28, 9, 8, 0, 8, 0, 91, 9, 20, 36, 8, 0, 8, 12, 0, 80, 9, 80, 8, 9, 8, 28, 15, 0, 91, 9, 8, 45, 8, 0, 0, 15, 0, 20, 8, 0
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OFFSET

0,5


COMMENTS

If such an m>0 exists, this proves that n is not in A051214, i.e., not of the form 3^xy^2. On the other hand, if there are integers x, y such that n=3^xy^2, then we know that a(n)=0.


LINKS



EXAMPLE

See A200507 for developed examples.
Some of the larger values include a(107)=17732, a(146)=1924, a(347)=4400, a(416)=2044, a(458)>30000.


PROG

(PARI) A200523(n, b=3, p=3)={ my( x=0, qr, bx, seen ); for( m=3, 9e9, while( x^p < m, issquare(b^xn) & 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))}


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



