#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 →

#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 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 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 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 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 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 →