49 is the first square, other than 1, whose digits are squares.
49 is the smallest number with the property that it, the number below it, and the number above it, all have a square of a prime as a factor.
49 is the smallest number with exactly eight representations as a sum of three distinct primes: 49 = 3 + 5 + 41 = 3 + 17 + 29 = 5 + 7 + 37 = 5 + 13 + 31 = 7 + 11 + 31 = 7 + 13 + 29 = 7 + 19 + 23 = 13 + 17 + 19.
49 is the smallest composite number that is not divisible by any Fibonacci number greater than 1.
49 is the largest prime square which is greater than the product of all lesser primes.
Just found an interesting site with number trivia. This link is about 49. I got a 70%.
ReplyDeletehttp://www.purposegames.com/game/number-trivia-49
Your first fact, "49 is the first square, other than 1, whose digits are squares," is incorrect. 4 and 9 are squares whose digits are squares.
ReplyDeleteOops - you are right.
DeleteYou could say that it's the first multi-digit square whose digits are all squares. It's trivial that any single-digit square consists of digits that are all squares. So the multi-digit case is the only kind that's at all interesting.
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