Today is 26 day of the year.
26 = 2 x 13
26 = 3 + 5 + 7 + 11, i.e. the sum of four consecutive primes.
26 is the fifth cake number, i.e. one can cut a cake into 26 pieces with five cuts.
26 is the sixth Eulerian number.
26 is the only natural number to be sandwiched between a square and a cube which implies that there is only one solution to x^2 + 1 = y^3 - 1where x and y are natural numbers; proof anyone?
If one considers the permutation of a set of four elements then some of the permutations are self-inverse. For example the permutation of the ordered set (a,b,c,d} into {c,d,a,b} can be described as the swapping of the first and third elements with a swapping of the fourth and second elements. If one was to repeat these two swaps on the set {c,d,a,b} then the set {a,b,c,d} would be the result. Thus the permutation is self-inverse.
The number self-inverse sets, or involutions, of five elements is 26.
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