Copyright © University of Cambridge. All rights reserved.

'Janine's Conjecture' printed from http://nrich.maths.org/

Show menu

Janine noticed, while studying some cube numbers, that ``if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number cubed''; e.g., 3, 4, 5 gives 3 x 4 x 5 + 4 = 64, which is a perfect cube. Does this always work? Can you prove or disprove this conjecture?