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# Category Archives: primes

## Fun with repunit divisors: more solutions

In Fun with repunit divisors I posed the following challenge: Prove that every prime other than 2 or 5 is a divisor of some repunit. In other words, if you make a list of the prime factorizations of repunits, every … Continue reading

Posted in arithmetic, iteration, modular arithmetic, number theory, primes, programming, proof, solutions
Tagged repunit

## Fun with repunit divisors: proofs

As promised, here are some solutions to the repunit puzzle posed in my previous post. (Stop reading now if you don’t want to see solutions yet!) Prove that every prime other than 2 or 5 is a divisor of some … Continue reading

Posted in iteration, modular arithmetic, number theory, pattern, primes, proof
Tagged divisibility, Fermat, prime, proof, repunit
1 Comment

## Fun with repunit divisors

In honor of today’s date (11/11/11), here’s a fun little problem (and some follow-up problems) I’ve seen posed in a few places (for example, here is a very similar problem). If I recall correctly, it was also a problem on … Continue reading

Posted in arithmetic, challenges, modular arithmetic, number theory, primes
Tagged divisors, primes, repunit
16 Comments

## Triangunit divisors and quadratic reciprocity

Recall that the triangunit numbers are defined as the numbers you get by appending the digit 1 to the end of triangular numbers. Put another way, where denotes the th triangular number, and the th triangunit number. The challenge, posed … Continue reading

Posted in arithmetic, modular arithmetic, number theory, primes, proof
Tagged OEIS, quadratic, reciprocity, triangular, triangunit
5 Comments

## Prime Time in Haskell

In a recent blog post, Patrick Vennebush of Math Jokes 4 Mathy Folks noted that 2011 can be expressed as a sum of consecutive prime numbers, and challenged his readers to work out how. He also posed a couple further … Continue reading

Posted in arithmetic, number theory, primes, programming
Tagged consecutive, Haskell, primes, sum
8 Comments

## Book Review: The Mystery of the Prime Numbers

Several months ago, Matthew Watkins sent me a review copy of his new book, Secrets of Creation Volume One: The Mystery of the Prime Numbers. It’s taken me a while to get around to reviewing it, but not for lack … Continue reading

Posted in books, number theory, primes, review
Tagged book review, mystery, numbers, prime
3 Comments

## MMM #33: Super divisible

This week’s Monday Math Madness is up at Wild About Math!. Looks like a fairly accessible problem this week: What’s the prime factorization of the smallest whole number that is divisible by all integers from 1 up to and including … Continue reading

Posted in challenges, links, number theory, primes
Tagged divisible, factorization, smallest