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Mr Honner
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Mr Honner
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2025-12-20 10:38:20
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Mr Honner Mr Honner Toggle Navigation About Resources Photography Writing Search for: Challenge Numbers 2024 and Differences of Squares — Solution The new year 2024 is a difference of squares, , which got me thinking about a fun little number theory problem : Is there a largest number that can not be expressed as the difference of squares? If so, find it. If not, prove no such number exists. Good luck, and happy new year! As promised, here’s my solution. There are infinitely many numbers that can not be expressed as a difference of squares. In fact, we can completely characterize numbers that can be expressed as a difference of squares and those that can’t. It all starts with factoring. Differences of squares have a useful structure that can be exposed by factoring: We can leverage this structure to answer our question. Suppose n can be factored as . If n can be expressed as a difference of squares, then we can also write Now set and . T...
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