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## Question

M and N are positive integers such that the sum of M cube and 101 is N square.

Find the smallest N.

Edited by Andrew1258

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n=926

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I got 926, just filling a quick excel spreadsheet

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The smallest number is 95

Kazal guha

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The smallest number is 51.

Use the a2-b2=(a+b)(a-b).

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51 is not only the smallest number, but the one and only number for n.

There is no other solution.

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It makes me sick that you all overlooked 10. Especially Balint who is way off the mark. -1 cubed is -1

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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 by jagdmc
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Ignore this edited post, my spreadsheet had an error. 95 and 926 are correct.

Edited by mungbean
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Ohh, cubed.

I misunderstood the word "cubed", I thought the concept "squared".

So, I have solved another problem.

Damn.

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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...

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