A pair of integers, such as 10 and 2, fulfills the condition that their difference results in an integer greater than only one of the original integers.
Let's break down why this works and how to find such integer pairs:
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The Difference: The difference between two integers, a and b, can be expressed as |a - b|. This ensures we are dealing with a positive difference (or zero).
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The Condition: We need |a - b| to be greater than either a or b, but not both.
Explanation with the Example (10 and 2):
- The difference: |10 - 2| = 8
- Is 8 > 10? No.
- Is 8 > 2? Yes.
Therefore, the difference (8) is greater than only one of the original integers (2), satisfying the condition.
How to Find Such Pairs:
The key is to have one number significantly larger than the other, but not so much that their difference exceeds both. Here are some approaches:
- Choose a small integer (e.g., 1, 2, 3) and a larger integer that isn't too much bigger. Trying a few values around that small integer will help you find a suitable pair.
- Consider negative numbers. For instance, consider 1 and -5. The absolute difference is |1 - (-5)| = 6. 6 is greater than 1, but it is not greater than -5.
Examples of Valid Pairs:
- (5, 1): |5 - 1| = 4. 4 > 1, but 4 < 5.
- (1, -3): |1 - (-3)| = 4. 4 > 1, but 4 > -3 (Note: This pair does NOT satisfy the only one condition)
- (-1, -5): |-1 - (-5)| = 4. 4 > -5, but 4 > -1. (Note: This pair does NOT satisfy the only one condition)
General Condition for Integers a and b:
|a - b| > a XOR |a - b| > b
Where XOR is a logical operator indicating that either the first statement or the second statement must be true, but not both.
This condition encapsulates the requirement that the absolute difference is greater than only one of the integers.
