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# integers

## Latest Articles

### The Hidden Connection That Changed Number Theory

Quadratic reciprocity lurks around many corners in mathematics. By proving it, number theorists reimagined their whole field.

### Two Students Unravel a Widely Believed Math Conjecture

Mathematicians thought they were on the cusp of proving a conjecture about the ancient structures known as Apollonian circles. But a summer project would lead to its downfall.

### 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.

### 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.

### The Map of Mathematics

Explore our surprisingly simple, absurdly ambitious and necessarily incomplete guide to the boundless mathematical universe.

### 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.

### The Fabulously Fair Feast

For this month’s puzzle, design a Sudoku square to figure out the likes and dislikes of four finicky friends.

### 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.

### 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?