# Posted in April 2012 …

## #math trivia #65 solution

Burt Kaliski Jr. (@modulomathy) 3/5/12 1:05 PM #math trivia for #March5: #65 = (x^2-xy+y^2)(x+y) for positive integers x, y. What are x and y? (Hint: simplify the product.) Simplifying the product by multiplying the terms gives 65 = x^3+y^3 The solution is x = 4, y = 1, or vice versa.

## #math trivia #64 solution

Burt Kaliski Jr. (@modulomathy) 3/4/12 8:08 PM #math trivia for #March4: #64 is one of only two sixth powers this year. How many days are nth powers for some n > 1? Seven days have numbers that are higher powers of 2: 4, 8, 16, 32, 64, 128, 256. There are four higher powers of … Continue reading

## #math trivia #63 solution

Burt Kaliski Jr. (@modulomathy) 3/3/12 5:08 PM #math trivia for #March3: #63 is not a #Mersenne prime but it’s divisible by two of them. Which ones? (Mersenne p = 2^q-1, p, q prime.) The day’s number, 63, has the form 2^6-1, but neither the exponent 6 nor the number 63 is prime. However, both prime … Continue reading

## #math trivia #62 solution

Burt Kaliski Jr. (@modulomathy) 3/2/12 9:09 PM #math trivia for #March2: #62 is 111110 base 2; with 5 ones this is “Hamming weight” 5. What other days this year have the same “weight”? The Hamming weight of an integer is the number of ones in its binary (base 2) representation. To find the different ways … Continue reading

## #math trivia #61 solution

Burt Kaliski Jr. (@modulomathy) 3/2/12 12:48 AM #math trivia for #March1: #61 is one sixth of the way through the year. Which other “sixths” come on the first day of the month? The last? A leap year has exactly six “sixths”, 61 days apart. With the usual alternation of 31- and 30-day months after February, … Continue reading

## #math trivia #60 solution

Burt Kaliski Jr. (@modulomathy) #math trivia for #February29: #60 shares a prime factor with 44 smaller integers. Which 16 smaller integers are relatively prime to 60? The 16 smaller (positive) integers that don’t share a prime factor with 60 are: 1, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 49, 53, … Continue reading

## #math trivia #59 solution

#math trivia for #February28:#59 and 61 are twin primes. What property of 60 makes this possible? (Hint:29 and 31 were also twins.) — Burt Kaliski Jr. (@modulomathy) February 28, 2012 The property of 60 that makes adjacent twin primes possible is that 60 is divisible by 6. If 60 were not divisible by 2, then … Continue reading

## #math trivia #58 solution

#math trivia for #February27: #58 is the 7th in the series 2 5 10 17 28 41 58. What’s the 8th? — Burt Kaliski Jr. (@modulomathy) February 27, 2012 A good starting point for answering a question about the next term in a series is to look at the differences between successive terms, which in this case is: 2 3 … Continue reading

## #math trivia #57 solution

#math trivia for #February26: #57 = 3*19 — a product using each odd digit once. Are there any other products of this form? — Burt Kaliski Jr. (@modulomathy) February 26, 2012 Let’s think about what a solution might look like. The general form needs to be ab = c*de where a, b, c, d and … Continue reading

## #math trivia #56 solution

#math trivia for #February25:  #56 is a product of consecutive numbers: 56 = 7*8. And 56 = ((7+8)^2)-1)/4.  What’s the general formula? — Burt Kaliski Jr. (@modulomathy) February 25, 2012 Replacing 7 with x and 8 with x+1 gives the general formula x(x+1) = ((x+(x+1))2-1)/4. Replacing x+(x+1) with 2x+1 on the right hand side gives … Continue reading