Difference between revisions of "2001 IMO Problems/Problem 6"

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6. <math>K > L > M > N</math> are positive integers such that <math>KM + LN = (K + L - M + N)(-K + L + M + N)</math>. Prove that <math>KL + MN</math> is not prime.
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== Problem 6 ==
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  <math>K > L > M > N</math> are positive integers such that <math>KM + LN = (K + L - M + N)(-K + L + M + N)</math>. Prove that <math>KL + MN</math> is not prime.
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==Solution==
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{{solution}}
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==See also==
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{{IMO box|num-b=5|num-a=6|year=2001}}
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[[Category: Olympiad Number Theory Problems]]

Revision as of 01:56, 6 October 2014

Problem 6

$K > L > M > N$ are positive integers such that $KM + LN = (K + L - M + N)(-K + L + M + N)$. Prove that $KL + MN$ is not prime.

Solution

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See also

2001 IMO (Problems) • Resources
Preceded by
Problem 5
1 2 3 4 5 6 Followed by
Problem 6
All IMO Problems and Solutions
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