Difference between revisions of "1967 IMO Problems/Problem 3"

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==Problem==
 
Let <math>k, m, n</math> be natural numbers such that <math>m+k+1</math> is a prime greater than <math>n+1.</math> Let <math>c_s=s(s+1).</math> Prove that the product <cmath>(c_{m+1}-c_k)(c_{m+2}-c_k)\cdots (c_{m+n}-c_k)</cmath> is divisible by the product <math>c_1c_2\cdots c_n</math>.
 
Let <math>k, m, n</math> be natural numbers such that <math>m+k+1</math> is a prime greater than <math>n+1.</math> Let <math>c_s=s(s+1).</math> Prove that the product <cmath>(c_{m+1}-c_k)(c_{m+2}-c_k)\cdots (c_{m+n}-c_k)</cmath> is divisible by the product <math>c_1c_2\cdots c_n</math>.
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==Solution==
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{{solution}}
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==See Also==
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{{IMO box|year=1967|num-b=1|num-a=3}}
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[[Category:Olympiad Geometry Problems]]

Revision as of 14:53, 17 February 2018

Problem

Let $k, m, n$ be natural numbers such that $m+k+1$ is a prime greater than $n+1.$ Let $c_s=s(s+1).$ Prove that the product \[(c_{m+1}-c_k)(c_{m+2}-c_k)\cdots (c_{m+n}-c_k)\] is divisible by the product $c_1c_2\cdots c_n$.

Solution

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See Also

1967 IMO (Problems) • Resources
Preceded by
Problem 1
1 2 3 4 5 6 Followed by
Problem 3
All IMO Problems and Solutions