Number Gossip
(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)
Unique Properties of 75
- 75 is the smallest pandigital number in base 4: 75 is written as 1023 in base 4 and contains all the possible digits
- 75 is the smallest numbers that is a sum of three distinct squares forming an arithmetic progression: 75 = 1 + 25 + 49
- 75 is the smallest composite deficient number whose sum as well as product of aliquot divisors is a perfect square
- There are 75 exceptional uniform polyhedra (that do not belong to infinite classes of prisms and antiprisms)
- 75 is the number of ways to rank four participants allowing for ties