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Broad Topics > Advanced Algebra > Remainder Theorem

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Interpolating Polynomials

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.

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Novemberish

Stage: 4 Challenge Level: Challenge Level:1

a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number. (b) Prove that 11^{10}-1 is divisible by 100.