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Omni-MATH / Suppose a,b and c are integers such that the greatest common divisor of x²+ax+b and x²+bx+c is x+1 (in the ring of polynomials in x with integer coefficients), and the least common…

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problem

Suppose a,ba, b and cc are integers such that the greatest common divisor of x2+ax+bx^{2}+a x+b and x2+bx+cx^{2}+b x+c is x+1x+1 (in the ring of polynomials in xx with integer coefficients), and the least common multiple of x2+ax+bx^{2}+a x+b and x2+bx+cx^{2}+b x+c is x3−4x2+x+6x^{3}-4 x^{2}+x+6. Find a+b+ca+b+c.
Plain-text mathematical notation (without MathML)
Suppose a,b and c are integers such that the greatest common divisor of x²+ax+b and x²+bx+c is x+1 (in the ring of polynomials in x with integer coefficients), and the least common multiple of x²+ax+b and x²+bx+c is x³−4x²+x+6. Find a+b+c.
Original LaTeX notation
Suppose $a, b$ and $c$ are integers such that the greatest common divisor of $x^{2}+a x+b$ and $x^{2}+b x+c$ is $x+1$ (in the ring of polynomials in $x$ with integer coefficients), and the least common multiple of $x^{2}+a x+b$ and $x^{2}+b x+c$ is $x^{3}-4 x^{2}+x+6$. Find $a+b+c$.

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Source and history

task_id
76d6a024-09ac-545b-92f3-de0d9beb8205
task_key
test--76d6a024-09ac-545b-92f3-de0d9beb8205
task_revision_id
1
config / split
/ test

Official source

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