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== | ||
| + | {{solution}} | ||
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| + | ==See Also== | ||
| + | |||
| + | {{IMO box|year=1967|num-b=1|num-a=3}} | ||
| + | [[Category:Olympiad Geometry Problems]] | ||
Revision as of 13:53, 17 February 2018
Problem
Let 
be natural numbers such that 
is a prime greater than 
Let 
Prove that the product ![\[(c_{m+1}-c_k)(c_{m+2}-c_k)\cdots (c_{m+n}-c_k)\]](http://latex.artofproblemsolving.com/d/e/a/dea859fcc8d7deb3466f7fb2394c0800dc8a55e4.png)
is divisible by the product 
.
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 | ||
