A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems. Joseph Silverman remembers when he began connecting ...

Consider this sequence of numbers: 5, 7, 9. Can you spot the pattern? Here’s another with the same pattern: 15, 19, 23. One more: 232, 235, 238. “Three equally spaced things,” says Raghu Meka, a ...

In positional systems, as mentioned earlier, the number represented is multiplied by the base each time you move to the left of a position and is always divided by the base each time you move to the ...

The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory. The rational numbers are the most familiar numbers: 1, -5, ½, and every ...