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MATH / Find the smallest positive integer n with the property that the polynomial x⁴−nx+63 can be written as a product of two nonconstant polynomials with integer coefficients.

Problem

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problem

Find the smallest positive integer nn with the property that the polynomial x4−nx+63x^4 - nx + 63 can be written as a product of two nonconstant polynomials with integer coefficients.
Plain-text mathematical notation (without MathML)
Find the smallest positive integer n with the property that the polynomial x⁴−nx+63 can be written as a product of two nonconstant polynomials with integer coefficients.
Original LaTeX notation
Find the smallest positive integer $n$ with the property that the polynomial $x^4 - nx + 63$ can be written as a product of two nonconstant polynomials with integer coefficients.

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
65aa7809-aae5-552e-a2f1-733004b0bf5e
task_key
intermediate~5falgebra--test--65aa7809-aae5-552e-a2f1-733004b0bf5e
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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