Guest Posted January 15, 2010 Report Share Posted January 15, 2010 (edited) M and N are positive integers such that the sum of M cube and 101 is N square. Find the smallest N. Edited January 15, 2010 by Andrew1258 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2010 Report Share Posted January 15, 2010 n=926 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2010 Report Share Posted January 15, 2010 I got 926, just filling a quick excel spreadsheet Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2010 Report Share Posted January 15, 2010 The smallest number is 95 Kazal guha Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2010 Report Share Posted January 15, 2010 The smallest number is 51. Use the a2-b2=(a+b)(a-b). Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2010 Report Share Posted January 15, 2010 51 is not only the smallest number, but the one and only number for n. There is no other solution. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2010 Report Share Posted January 15, 2010 It makes me sick that you all overlooked 10. Especially Balint who is way off the mark. -1 cubed is -1 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2010 Report Share Posted January 15, 2010 (edited) m=95; n=926. Ok, I cheated on this one, since I don't know of an efficient way to estimate this number, different from using an Excel spreadsheet. If it wasn't for the riddle's condition "positive integers", then m=-1; n=10 would have been the easiest answer... Anyway, how were we supposed to come up with the actual answer without cheating?? Edited January 15, 2010 by jagdmc Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2010 Report Share Posted January 15, 2010 (edited) Ignore this edited post, my spreadsheet had an error. 95 and 926 are correct. Edited January 15, 2010 by mungbean Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2010 Report Share Posted January 15, 2010 Ohh, cubed. I misunderstood the word "cubed", I thought the concept "squared". So, I have solved another problem. Damn. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 15, 2010 Report Share Posted January 15, 2010 It makes me sick that you all overlooked 10. Especially Balint who is way off the mark. -1 cubed is -1 Except for the fact that M and N are both positive integers... Quote Link to comment Share on other sites More sharing options...
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M and N are positive integers such that the sum of M cube and 101 is N square.
Find the smallest N.
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