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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2022 • Question 1

Question

Math 6310 • Algebra Spring 2022 • Question 1

Consider the ideal \(I:=(2x-9,3x-7)\) in the ring \(\mathbb {Z}[x]\). Find the smallest positive integer \(n\) such that

\[ (x^{26}+x+1)^{13}-n \]

belongs to the ideal \(I\).

Raw LaTeX

Consider the ideal \(I:=(2x-9,3x-7)\) in the ring \(\mathbb{Z}[x]\). Find the smallest positive integer \(n\) such that

\[
(x^{26}+x+1)^{13}-n
\]


belongs to the ideal \(I\).

Topic Tags

Ideals and Quotient Rings Ideals in Quadratic Integer Rings and Exterior Powers Polynomial Rings and Ring Homomorphism Kernels