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Old 05-13-2008   #80
theredsky
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first, you factor 24 = 2^3 * 3
So the next perfect cube would be 2^a multiple of three * 3^3
The answer is 24 * 9, which is equal to 216

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WITH FULL SOLUTIONS PLEASE

Fractions a/b and c/d are called neighbor fractions if their difference (ad - bc)/(bd) has a numerator of positive or negative 1, that is, ad - bc = positive or negative one. Prove that

If a/b and c/d are neighbor fractions, then (a + b)/(c + d) is between them and is a neighbor fraction for both a/b and c/d; moreover, no fraction e/f with positive integer "e" and "f" such that f is less than b + d is between a/b and c/d. [/img]