Dr P & ICot among others
It’s great to see people who love math!
Here are some interesting mathematical properties, but not necessarily “mixups”:
16- is the only integer where m to the nth power = n to the mth power (2 to the 4th power or 4 to the 2nd power)
17 -is the first number that can be written as the sum of a positive cube and a positive square in two different ways; that is, the smallest n such that x3 + y2 = n has two different solutions for x and y positive integers. The next such number is 65.(2cubed plus 3squared (8+9) or 1cubed plus 4squared (1+16))
23- The sum of the first 23 primes is 874, which is divisible by 23!
24- the product of any 4 consecutive numbers must be divisible by 24
25- is a perfect square (5*5) & is the sum of 2 perfect squares: 3squared(3×3=9) + 4squared(4×4=16)
36- is a square triangular number, i.e., it can be represented as both a square & triangle using x’s (or o’s)
(I tried the triangle above..try it yourself, you should get it!)
x x x x x x
x x x x x x
x x x x x x
x x x x x x
x x x x x x
x x x x x x
.
x
x x
x x x
x x x x
x x x x x
x x x x x x
x x x x x x x
x x x x x x x x
36- multiplied by any other number always produces a quotient whose individual digits add up to nine:
36 x 2 = 72 (7 + 2 = 9)
36 x 36 = 1296 (1 + 2 + 9 + 6 = 18) (1 + 8 = 9)
36 – is the smallest integer which can be expressed as the sum of consecutive primes in 2 ways:
36= 5 + 7 + 11 + 13
and
36= 17 + 19
37 -is the only two digit number (in base 10) that when you multiply by 2 and subtract 1, results in the original number backwards!!!
37- is the only two digit number (in base 10) with the following property:
The difference between the two digits (absolute value) equals the square root of the difference between the original number and the least common multiple of the two digits.
7-3=4
4squared = 16
7 x 3 = 21 (least common multiple)
37 – 21 = 16
square root of 16 = 4!
37- very interesting mathematical properties of 37:
111: 1+1+1=3 and 3 x 37 = 111
222: 2+2+2=6 and 6 x 37 = 222
333: 3+3+3=9 and 9 x 37 = 333
…
999: 9+9+9=27 and 27 x 37 = 999
44- is a happy number (replace 44 by the sum of the squares of its digits, and repeat the process until it equals 1)
4squared + 4squared = 16+16=32
3squared + 2squared = 9+4=13
1squared + 3squared = 1+9=10
1squared + 0squared = 1+0=1
44- the number of derangements of 5 items (44 permutations where none of the elements appear in their original position)
***TRY IT! IT’S FUN!***
HINT:
9 is the number of derangements of 4 items ABC&D:
BADC, BCDA, BDAC,
CADB, CDAB, CDBA,
DABC, DCAB, DCBA
(all other permutations result in at least one in the original position)
45- the sum of the digits 987654321 is 45.
the sum of the digits 123456789 is 45.
The difference between these 2 numbers is 864197532…
GUESS WHAT!
This difference also adds up to 45!!!
48- is a semi-perfect number (equals the sum of some/all of its divisors)
Its 10 divisors are 1,2,3,4,6,8,12,16,24,&48 (1×48, 2×24, 3×16, 4×12, & 6×8)
48= 2+4+6+12+24
49- is the first square (7×7) where the digits (4&9) are also squares
49- the sum of the digits of 49squared (2401: 2+4+0+1=7) is the square root of 49 (7×7=49)! AMAZING!