#math trivia for #May13:  #134 and its prime divisors (67, 2) have no common digits.  When did this last happen?  When will it happen again? Answer:  This is a fun problem that can be solved with by trial-and-error moving forward and backward from 134, using some properties of factorizations to shorten the search. Clearly, a … Continue reading →

#math trivia for #May12:  #133 has the form xyz where xyz is one more than a multiple of yz (133 = 4*33+1).  Which other day-numbers do? Answer:  If xyz is one more than a multiple of yz, then x00 = xyz = yz is also one more than a multiple of yz.  This means that … Continue reading →

#math trivia for #May11: #132 can be expressed in three ways as the product of positive integers x, y where x-y is a square.  What are they? Answer:  Consider the possible factorizations of 132 into x*y: 132*1 66*2 44*3 33*4 22*6 12*11 The three factorizations where x-y is a square are 66*2, 22*6, and 12*11.

#math trivia for #May10:  #131 is a prime, 13 is a prime, and 31 is a prime.  For what other day-numbers xyz are xyz, xy and yz all prime? Answer:  This is a good pattern matching problem.  The shortest approach is probably to look at prime xy values and see which z’s work.  We’ll allow … Continue reading →

#math trivia for #May9:  #130 can be expressed with two 1s and the rest (if any) all 0s in what bases? Answer.  This is equivalent to asking for which bases b can 130 be expressed as 130 = b^x + b^y for distinct x, y.  Without loss of generality, let y be the smaller of … Continue reading →

#math trivia for #May8: #129 is another prime of the form 2^x+1. How many others will be encountered this year? — Burt Kaliski Jr. (@modulomathy) May 8, 2012 Nine day-numbers have the form 2^x+1:  2, 3, 5, 9, 17, 33, 65, 129, and 257.  Of these, six are prime:  2, 3, 5, 17, 129 and … Continue reading →

#math trivia for #May7:  Similar to #127:  How can #128 be computed from 1, 2, and 8 using only two operations from +, -, *, /, ^? — Burt Kaliski Jr. (@modulomathy) May 7, 2012 There’s a small trick:  You have to use either parentheses or superscripts. 128 = 2^(8-1) or 128 = 28-1

#math trivia for #May6: How can #127 be computed from 1, 2, and 7 using only two operations from +, -, *, /, and ^ (exponentiation)? — Burt Kaliski Jr. (@modulomathy) May 6, 2012 Having exponentiation as an operator helps out here, because 2^7 = 128.  The answer is 2^7 – 1 = 127   … Continue reading →

#math trivia for #May5: #126 is one of 40 day-numbers divisible by 9. How many of the 40 also have a digit-sum of 9? — Burt Kaliski Jr. (@modulomathy) May 5, 2012 Every number divisible by 9 has a digit-sum that’s also divisible by 9.  For most small numbers divisible by 9, the digit-sum is … Continue reading →

#math trivia for #May4: #125 divides 1000. What other day-numbers divide a power of 10? What’s the general pattern these numbers follow? — Burt Kaliski Jr. (@modulomathy) May 4, 2012 The day-numbers that divide a power of 10 (and the power they divide) are: 1 — 1 2 — 10 4 — 100 5 — … Continue reading →