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#math trivia for #April26: #117 is one of 40 day-numbers divisible by 9 this year. How many also have digits that add up to 9? — Burt Kaliski Jr. (@modulomathy) April 26, 2012 Any number whose digits add up to a multiple of 9 is divisible by 9, and vice versa. Most of the day-numbers … Continue reading →

#math trivia for #April27: #118 is the sum of three squares (not necessarily distinct) in two different ways. What are they? — Burt Kaliski Jr. (@modulomathy) April 27, 2012 The two ways are: 118 = 1+36+81 118 = 9+9+100 One way to find the answers is to start by observing that at least one of … Continue reading →

#math trivia for #April28: #119 is the product of two primes differing by 10. Any other day-numbers of this type? — Burt Kaliski Jr. (@modulomathy) April 29, 2012 In other words, are there other day numbers of the form p*q where q = p+10 and p and q are both prime? The value of p … Continue reading →

Burt Kaliski Jr. (@modulomathy) 4/22/12 4:26 PM #math trivia for #April22: #113 is 16 weeks and 1 day, both squares. How many days of the year does this happen? The pattern happens twice during the week preceded by a square number of full weeks. There are eight square numbers between 0 and 52 inclusive, so … Continue reading →

Burt Kaliski Jr. (@modulomathy) 4/21/12 3:27 PM #math trivia for #April21: #112 is four times a perfect number. Does that make it more or less abundant? Is there a general rule? The divisors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, and 112. The sum of the divisors less than the … Continue reading →

Burt Kaliski Jr. (@modulomathy) 4/20/12 5:23 PM #math trivia for #April20: #111 is a prime in every base less than 10, except for which two? The base-10 values corresponding to 111 in bases 1 to 9 are 3,7,13,21,31,43,57,73,91 There are actually three non-primes in this list, the ones corresponding to bases 4, 7, and 9. … Continue reading →

#math trivia for #April19:#110 is 10*11, 2 more than 9*12, 6 more than 8*13, 12 more than 7*14, etc.What’s the pattern? — Burt Kaliski Jr. (@modulomathy) April 19, 2012 Let n be the index of the term, starting at 0.  The terms follow the pattern:   110 = (10-n)*(11+n) + n*(n+1) In other words, for … Continue reading →

#math trivia for #April17: #108 equals 2^2 * 3^3. What’s the next number that can be expressed as a product of x^x terms (x > 1)? — Burt Kaliski Jr. (@modulomathy) April 17, 2012 If a multi-term product is required, then the next number is 2^2 * 4^4, or 1024. If “products” with just one … Continue reading →