Minimize the number of roots

Algebra Level 5

Suppose p(x)p(x) and q(x)q(x) are polynomials of degree 100100 with complex coefficients, having no common zeroes. Find the smallest possible total number of complex zeroes of the polynomials p,p, q,q, and pq,p-q, counted without multiplicity.

Details and assumptions

When the zeroes are counted without multiplicity, the polynomial x2(x1)3x^2(x-1)^3 has two zeroes: x=0x=0 and x=1.x=1.

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