# Problem Solving Integers

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“It’s right at the frontier of what we can handle,” Browning added.

that have a remainder of 4 or 5 after being divided by 9.

The tools devised for such a proof might pry open the logic of the problem, or apply to other Diophantine equations.

Results like Booker’s for 33 offer support for this conjecture, giving number theorists more confidence that it’s a proof worth pursuing.

As you go below this level, the numbers are written as negatives.

They knew that 29 could be written as 3³ 1³ 1³, for instance, whereas 32 is not expressible as the sum of three integers each raised to the third power. Now, Andrew Booker, a mathematician at the University of Bristol, has finally cracked it: He discovered that (8,866,128,975,287,528)³ (–8,778,405,442,862,239)³ (–2,736,111,468,807,040)³ = 33.

The integers are often represented as equally spaced points on a number line , as shown in the figure. What number would you use to represent the position of the ball compared to ground level?

Does this number belong to the set of whole numbers? Usually, ground level is considered as height zero.

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