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Omni-MATH / Let a,b,c be positive integers. All the roots of each of the quadratics ax²+bx+c,ax²+bx−c,ax²−bx+c,ax²−bx−c are integers. Over all triples (a,b,c), find the triple with the third s…

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problem

Let a,b,ca, b, c be positive integers. All the roots of each of the quadratics ax2+bx+c,ax2+bx−c,ax2−bx+c,ax2−bx−ca x^{2}+b x+c, a x^{2}+b x-c, a x^{2}-b x+c, a x^{2}-b x-c are integers. Over all triples (a,b,c)(a, b, c), find the triple with the third smallest value of a+b+ca+b+c.
Plain-text mathematical notation (without MathML)
Let a,b,c be positive integers. All the roots of each of the quadratics ax²+bx+c,ax²+bx−c,ax²−bx+c,ax²−bx−c are integers. Over all triples (a,b,c), find the triple with the third smallest value of a+b+c.
Original LaTeX notation
Let \(a, b, c\) be positive integers. All the roots of each of the quadratics \(a x^{2}+b x+c, a x^{2}+b x-c, a x^{2}-b x+c, a x^{2}-b x-c\) are integers. Over all triples \((a, b, c)\), find the triple with the third smallest value of \(a+b+c\).

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task_id
e0aa271e-98ca-5081-bf91-b69aa68d0981
task_key
test--e0aa271e-98ca-5081-bf91-b69aa68d0981
task_revision_id
1
config / split
/ test

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