# Posted in July 2012 …

## #math trivia #134 solution

#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 #133 solution

#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 #132 solution

#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 #131 solution

#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 #130 solution

#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