#math trivia for #February17: #48 is very abundant — its divisors add up to 124. How do you go from 48 = 16*3 to 124 = 31*4? — Burt Kaliski Jr. (@modulomathy) February 17, 2012 A perfect number n one whose smaller divisors add up to n. The first two perfect numbers are 6 (smaller … Continue reading

# Posted in March 2012 …

## #math trivia #47 solution

#math trivia for #February16: 47 is the third prime this “decade” (the 40s). Why are the 10s, 40s and 70s so popular for primes? — Burt Kaliski Jr. (@modulomathy) February 16, 2012 The 10s, 40s and 70s each have at least three primes: 10s: 11, 13, 17, 19 40s: 41, 43, 47 70s: 71, 73, … Continue reading

## #math trivia #46 solution

#math trivia for #February15: 46 is a nontrivial (multi-digit) palindrome in base 4 (46 = 232 base 4) and which four other bases? — Burt Kaliski Jr. (@modulomathy) February 15, 2012 A positive integer x can be expressed in any base b ≥ 2 as a sum of weighted powers x = dk-1 bk-1 + dk-2 bk-2 … Continue reading

## #math trivia #45 solution

#math trivia for #February14: 45 is the 9th triangular number: 45 = 1+2+3+…+9. How do you make a 9×9 square out of 45-unit triangles? — Burt Kaliski Jr. (@modulomathy) February 15, 2012 The nth triangular number has the form 1+2+3+…+n, and is so named because it measures the “units” in a triangularly shaped figure with … Continue reading

## #math trivia #44 solution

#math trivia for #February13: 44 is the fifth number of the form p^2*q for distinct primes p, q. What are p and q? What were the first four? — Burt Kaliski Jr. (@modulomathy) February 13, 2012 Factoring the day’s number, 44, quickly yields the values of p and q: 44 = 2^2 * 11 , … Continue reading

## #math trivia #43 solution

#math trivia for #February12:43 is the smallest number of form p^4+q^3 where p, q are prime. What are p and q? What’s the next number? — Burt Kaliski Jr. (@modulomathy) February 12, 2012 This is a quick one. If 43 is the smallest number of the given form, then p, having the larger exponent, must be the smallest … Continue reading

## #math trivia #42 solution

#math trivia for #February11:42 is the second smallest tricomposite:42 = 2*3*7; what are its eight divisors? — Burt Kaliski Jr. (@modulomathy) February 11, 2012 Tricomposite is not in the dictionary, but its definition should be clear from context: a tricomposite number is the product of three primes. Bicomposite numbers are common in cryptography — the … Continue reading

## Here They Come: Solutions to the Daily Math Trivia

It’s been about six weeks since I started posing questions in my daily math trivia tweets rather than just sharing observations about the number of the day, so it seemed like a good time to start giving answers. My math trivia tweets started originated in an exchange on Friday, January 13, with a friendly security guard at … Continue reading

## Surely You’re Joking

For my birthday this year, my sister gave me a copy of Surely You’re Joking, Mr. Feynman. In Part 1, subtitled “From Far Rockaway to MIT,” the famous physicist describes how at age 11 or 12 he built his own electrical circuit with lamps and switches. At around the same age, I built a circuit … Continue reading