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# Janine's Conjecture

##### Age 14 to 16Challenge Level

Julia of Downe House School gave the neatest solution to this problem by substituting 'x-1', 'x', 'x+1' for the three consecutive numbers and giving the following statement of Janine's conjecture:

( x - 1) x ( x + 1) + x = x 3 .

This is Julia's proof:

( x - 1) ( x + 1) = x 2 - 1
and
( x 2 - 1) x = x 3 - x .

Therefore ( x - 1) x ( x + 1) + x = x 3 .

So Janine's conjecture will always work whichever three consecutive numbers are chosen.