A200520 -id:A200520 - 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.

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, 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, 4, 7, 7, 8, 4, 16, 7, 0, 4, 7, 9, 8, 4, 7, 0, 7, 4, 32

Offset: 0

M. F. Hasler, Nov 18 2011

nonn

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.

			See A200512 for motivation and detailed examples.

M. F. Hasler, Table of n, a(n) for n = 0..1000

Cf. A051204-A051221, A200505-A200520.

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 & break; next(3))); return(m))}

A200519 Least m>0 such that n = y^2 - 9^x (mod m) has no solution, or 0 if no such m exists.

Original entry on oeis.org

0, 4, 4, 0, 8, 4, 4, 0, 0, 4, 4, 9, 8, 4, 4, 0, 0, 4, 4, 0, 8, 4, 4, 9, 0, 4, 4, 0, 8, 4, 4, 80, 9, 4, 4, 0, 8, 4, 4, 63, 0, 4, 4, 80, 8, 4, 4, 9, 0, 4, 4, 45, 8, 4, 4, 0, 9, 4, 4, 9, 8, 4, 4, 0, 133, 4, 4, 80, 8, 4, 4, 15, 0, 4, 4, 63, 8, 4, 4

Offset: 0

M. F. Hasler, Nov 18 2011

nonn

To prove that an integer n is in A051211, it is sufficient to find integers x,y such that y^2 - 9^x = n. In that case, a(n)=0. To prove that n is *not* in A051211, it is sufficient to find a modulus m for which the (finite) set of all possible values of 9^x and y^2 (mod m) allows us to deduce that y^2 - 9^x can never equal n. The present sequence lists the smallest such m>0, if it exists.

			See A200512 for motivation and detailed examples.

Cf. A051204-A051221, A200505-A200520.

A200519(n,b=9,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 & break; next(3))); return(m))}

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.

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