Tag Archives: Polynomials

[Soln] 2013 AIME I Problem 10

Posted on 13 Jun 2016 by kjytay

2013 AIME I 10. There are nonzero integers , , , and  such that the complex number  is a zero of the polynomial . For each possible combination of  and , let  be the sum of the zeroes of .Find the sum … Continue reading →

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2013 AIME I Problem 10

Posted on 13 Jun 2016 by kjytay

2013 AIME I 10. There are nonzero integers , , , and  such that the complex number  is a zero of the polynomial . For each possible combination of  and , let  be the sum of the zeroes of .Find the sum … Continue reading →

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[Soln] Find f(-100)

Posted on 30 Apr 2016 by kjytay

Let be a polynomial such that Find . (Credits: I learnt of this problem from Zi Song Yeoh on brilliant.org.)

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Find f(-100)

Posted on 29 Apr 2016 by kjytay

Let be a polynomial such that Find . (Credits: I learnt of this problem from Zi Song Yeoh on brilliant.org.)

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[Soln] 2016 Canadian Math Olympiad Problem 3

Posted on 22 Apr 2016 by kjytay

2016 Canada MO 3. Find all polynomials with integer coefficients such that is a prime number for infinitely many integers .

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[Hints] 2016 Canadian Math Olympiad Problem 3

Posted on 22 Apr 2016 by kjytay
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2016 Canadian Math Olympiad Problem 3

Posted on 21 Apr 2016 by kjytay

2016 Canada MO 3. Find all polynomials with integer coefficients such that is a prime number for infinitely many integers .

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[Soln] 2015 Spain MO Day 1 Problem 1

Posted on 19 Oct 2015 by kjytay

2015 Spain MO 1.1. On the graph of a polynomial with integer coefficients, two points are chosen with integer coordinates. Prove that if the distance between them is an integer, then the segment that connects them is parallel to the horizontal axis.

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2015 Spain MO Day 1 Problem 1

Posted on 18 Oct 2015 by kjytay

2015 Spain MO 1.1. On the graph of a polynomial with integer coefficients, two points are chosen with integer coordinates. Prove that if the distance between them is an integer, then the segment that connects them is parallel to the horizontal axis.

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[Soln] 2015 AIME II Problem 6

Posted on 14 Jul 2015 by kjytay

2015 AIME II 6. Steve says to Jon, “I am thinking of a polynomial whose roots are all positive integers. The polynomial has the form for some positive integers and . Can you tell me the values of and ? After … Continue reading →

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