A345894 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A345894

Positive integers representable by the two cyclotomic binary forms Phi_5(x,y) and Phi_12(u,v).

1, 16, 61, 81, 256, 625, 976, 1296, 2401, 4096, 4941, 6561, 10000, 14641, 15616, 20736, 28561, 38125, 38416, 50625, 65536, 79056, 83521, 104976, 130321, 146461, 160000, 194041, 194481, 229981, 234256, 249856, 279841, 331776, 390625, 400221, 456976, 531441

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Positive integers C such that Phi_5(x,y) = Phi_12(u,v) = C has a solution with nonzero (x,y,u,v).

A cyclotomic binary form over Z is a homogeneous polynomial in two variables which has the form f(x, y) = y^EulerPhi(k)*CyclotomicPolynomial(k, x/y) where k is some integer >= 3. An integer n is represented by f if f(x,y) = n has an integer solution.

LINKS

Table of n, a(n) for n=1..38.

Étienne Fouvry, Claude Levesque and Michel Waldschmidt, Representation of integers by cyclotomic binary forms, arXiv:1712.09019 [math.NT], 2017.

EXAMPLE

Phi_5(1,-3) = 1^4 + 1^3*(-3) + 1^2*(-3)^2 + 1*(-3)^3 + (-3)^4 = 1 - 3 + 9 - 27 + 81 = 61 and Phi_12(2, 3) = 2^4 - 2^2*3^2 + 3^4 = 16 - 36 + 81 = 61, so 61 is a term.

CROSSREFS

Cf. A296095.

Sequence in context: A296958 A258731 A316125 * A039406 A031190 A043229

Adjacent sequences: A345891 A345892 A345893 * A345895 A345896 A345897

KEYWORD

nonn

AUTHOR

Shashi Kant Pandey, Jul 23 2021

EXTENSIONS

a(8)-a(38) from Jon E. Schoenfield, Jul 24 2021

STATUS

approved