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integers
number theory
Mathematicians Crack a Simple but Stubborn Class of Equations
Ever since Archimedes, mathematicians have been fascinated by equations that involve a difference between squares. Now two mathematicians have proven how often these equations have solutions, concluding a decades-old quest.
number theory
Math’s ‘Oldest Problem Ever’ Gets a New Answer
A new proof significantly strengthens a decades-old result about the ubiquity of ways to represent whole numbers as sums of unit fractions.
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The Map of Mathematics
Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.
Insights puzzle
Solution: ‘The Fabulously Fair Feast’
The solution to this month’s puzzle explains how to design a Sudoku square to figure out the likes and dislikes of four or eight finicky friends.
Insights puzzle
The Fabulously Fair Feast
For this month’s puzzle, design a Sudoku square to figure out the likes and dislikes of four finicky friends.
Insights puzzle
Solution: ‘Be Still My Pulsating Sequence’
The solution to this month’s puzzle explains how to find a rule behind a given sequence of numbers and challenges readers to take on a ‘lovely’ unsolved problem.
Insights puzzle
Be Still My Pulsating Sequence
Can you infer the simple rule behind a number sequence that spikes up and down like the beating of a heart?