For each integer a ≥ 1, the affine Erdős Problem 270 constants C(a,0), …, C(a,a−1), C(a,a+1) are algebraically independent; every other C(a,b) with b ≥ 1−a is a nonconstant rational affine combination of them and is transcendental.
For each integer a ≥ 1, the affine Erdős Problem 270 constants C(a,0), …, C(a,a−1), C(a,a+1) are algebraically independent; every other C(a,b) with b ≥ 1−a is a nonconstant rational affine combination of them and is transcendental.
For each integer a ≥ 1, the affine Erdős Problem 270 constants C(a,0), …, C(a,a−1), C(a,a+1) are algebraically independent; every other C(a,b) with b ≥ 1−a is a nonconstant rational affine combination of them and is transcendental.
If correct, this settles the positive affine subfamily of Erdős Problem 270 much more strongly than irrationality, while the general nondecreasing-function question remains open.
Are the constants for positive affine choices f(n)=an+b algebraically independent in the stated fixed-slope basis, and thus individually transcendental?
Publication dates and editorial changes.
AI-led algebraic-independence claim for affine Erdős Problem 270
Allow optional Google Analytics to help improve AIProofWatch? Privacy details.
