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Let n and k be positive integers such that n<106 and (1313)+(1413)+(1513)++(5213)+(5313)+(5413)=(nk)
What is the ordered pair (n, k)?

 Feb 25, 2020
 #1
avatar+6251 
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Using the hockey stick identity54n=13(n13)=(54+113+1)=(5514)

 

https://en.wikipedia.org/wiki/Hockey-stick_identity

 Feb 25, 2020
 #2
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oh that makes sense to use the hockey stick identity. Thanks for the help!!

mathmathj28  Feb 25, 2020
 #3
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That's not an ordered pair though.

AnimalMaster  Feb 27, 2020
 #4
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The ordered pair would be (55, 14)

mathmathj28  Mar 4, 2020

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