Burt Kaliski Jr. (@modulomathy) 3/21/12 2:54 PM #math trivia for #March21: #81 is a square, and the sum of its digits is a square. What other days this year have this property? The one-digit squares all have this property: 1, 4, 9. Among the 15 other day-numbers not already mentioned that are squares, the ones … Continue reading →

Burt Kaliski Jr. (@modulomathy) 3/20/12 11:06 AM #math trivia for #March20: #80 has the form x^4-1 for x > 2 so must have at least three nontrivial divisors. What are they, and why three? The nontrivial divisors of 80 (those other than 80 or 1) are 2, 4, 5. 8, 10, 16, 20, and 40. … Continue reading →

Burt Kaliski Jr. (@modulomathy) 3/19/12 10:37 PM #math trivia for #March19: #79 has one of the highest digit sums of any two-digit prime: 7+9=16. Which two-digit prime has a higher sum? The only two-digit prime with a higher digit sum than 79 is 89. Indeed, the only two-digit numbers with a higher digit sum than … Continue reading →

Burt Kaliski Jr. (@modulomathy) 3/17/12 2:12 PM #math trivia for #March17: #77 is a product of two consecutive primes — fourth such product this year. How many more are there in 2012? There can’t be that many more, because we’re already up to 7*11, and the square root of 366 — the largest day-number this … Continue reading →

Burt Kaliski Jr. (@modulomathy) 3/16/12 1:12 PM #math trivia for #March16: #76 is one of the more common two-digit endings of squares between 1 and 999. What endings are more common? This problem looks at the range of numbers from 1 to 999 rather than the usual day-number range of 1 to 366 for a … Continue reading →

Burt Kaliski Jr. (@modulomathy) 3/14/12 3:17 PM #math trivia for #March14: Happy #PiDay — a much more fascinating number to ponder today than #74 Indeed, π, the ratio between the circumference of a circle and its diameter, is one of the most famous and useful numbers in mathematics. The closest approximation to π to two … Continue reading →

Burt Kaliski Jr. (@modulomathy) 3/13/12 7:42 AM #math trivia for #March13: #73 as a modulus gives square roots to -1. Solve x^2+1 = 0 (mod 73) where x is an integer between 0 and 72. One way to find the square root is by trial and error, looking for the smallest integer congruent to 72 … Continue reading →

Burt Kaliski Jr. (@modulomathy) 3/11/12 6:02 PM #math trivia for #March11: #71 is closest integer to sqrt(5000) — average 2 weeks per thousand. What’s the average for the next five? The “next five” here refers to the next five thousand, and the question is asking for the average number of weeks per thousand from sqrt(5000) … Continue reading →