*“They’re rich enough to simulate computers.” Diophantine equations are polynomial equations whose unknown variables must take integer values.*

*“They’re rich enough to simulate computers.” Diophantine equations are polynomial equations whose unknown variables must take integer values.*

The opposite of an integer is obtained by changing its sign. (a) The opposite of `-3` is `3` and (b) The opposite of `4` is ` -4`. We can change the subtraction into a more familiar addition by realising that subtracting an integer is the same as adding its opposite.

Notice that opposite is not the same as absolute value. (a) ` -2 5` means "start at `-2` and go `5` in the positive direction" So we have: It is -4° and snowing. (a) ` -4 - (-3) = -4 ( 3) = -1 ` (We added 3 because the opposite of -3 is 3.) (b) `5 - ( 7) = 5 (-7) = -2.` (We added -7 because the opposite of 7 is -7.

The forecast for tomorrow is for a rise in temperature of 6°. Eventually you’ll see the question is the same as "5 - 7" and we can do this as a journey: Start at 5 and move 7 units to the left.

Answer: -2.) When multiplying integers, we can think of multiplying "blocks" of negative numbers.

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Booker found this odd trio of 16-digit integers by devising a new search algorithm to sift them out of quadrillions of possibilities.

The algorithm ran on a university supercomputer for three weeks straight.

And 33 was an especially stubborn case: Until Booker found his solution, it was one of only two integers left below 100 (excluding the ones for which solutions definitely don’t exist) that still couldn’t be expressed as a sum of three cubes. [, or ten quadrillion, and just as far down into the negative integers — for the right numerical trio was computationally impractical until Booker devised his algorithm.

“He has not just run this thing on a bigger computer compared to the computers 10 years ago — he has found a genuinely more efficient way of locating the solutions,” said Tim Browning, a number theorist at the Institute of Science and Technology Austria.

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