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Sister Assumpta lectures 66 students on number theory. One day, she asked them to number themselves from 1 to 66 and then form 33 pairs such that the sum of the numbers assigned to...
In attempting to solve Bernardo Recaman Santos' question about triplets and quadruplets (in a row) of these numbers as an exercise for my puzzle club, I came up with a closest fit...
A solution to part of the Cohen-Lenstra conjecture helps resolve a long-standing mystery about quadratic forms
Years ago I wrote about Gilbreath’s conjecture. It’s a simple conjecture; you could explain it to anyone who understands what prime numbers are. See the linked post for a descripti...
You come across a written note in the course of your investigations. Most of the note is horribly smudged with no words immediately legible. If you do some analysis on the smudges,...
Squares, high and low Let p be an odd prime number. Then half the numbers from 1 through p − 1 are squares and half are not. That is, for half of numbers 1 ≤ k < p, the equation...
Eric Lu announced on X today that he has factored RSA-260, a number N with 260 digits (862 bits) that is the product of two large primes [1]. RSA numbers are challenge problems pos...
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