A. Common Results. (N<10)111/3N = 37
Any triple, repeating-digit number when divided by it's digital sum will give 37 as the answer.
E.G. 777 / 21 = 37, 999 / 27 = 37
B. Obvious Equality. x = xy(1/y)
Any number multiplied by any other number and then multiplied by it's reciprocal results in the original number.
E.G. 2 = 2 x 3 (1 / 3), 4 = 4 x 9 (1 / 9)
C. Cubic Loops sqrt(x)^3/x = sqrt(x)
When dividing the square root of a number that has been raised to the third power by the original number the result will be it's square root.
E. G. sqrt(9)^3 / 9 = sqrt(9) sqrt(4)^3 / 4 = sqrt(4)
D. Oddness Formula. 2N ± 1 = Odd
If you add or subtract 1 from any Natural number that has been doubled then the result will be an odd number
E.G. 2 x 6 ± 1 = 11 or 13, 2 x 9 ± 1 = 17 or 19
E. Novem Aureum. Fib12N mod 9 = 0
Every 12th number in the Fibonacci sequence is evenly divisible by 9.
E.G. 144 / 9 = 0, 46368 / 9 = 0
F. Sandwalk Sequence. (S1+2), (S2-1), (S3+2)...
Build the sequence starting at 1 then alternate between adding 2 then subtracting 1.
E.G. 1,3,2,4,3,5,4,6,5,7,9,8,10,9,11,10,12...