

A345894


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


0



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
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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



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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



