The polynomial [read slowly] x to the n plus y to the n is irreducible over the reals if and only if n is one of (-5[5])these numbers. Every known almost perfect number is one of (10[1]-5[12])these numbers. (-5[4])The cardinality of (-5[2])the (-5[1])power set of (-5[2])any (10[1]-5[3])finite set is one of (10[9]-5[10])these (10[1])numbers. These (10[3])numbers appear in (10[1])the exponent in the formula for (10[1])Fermat numbers, (-5[2])while (10[1]-5[1])Mersenne primes are defined as (10[1]-5[2])being (10[5]-5[1])one (10[4])less (10[2]-5[1])than (10[10]-5[4])these (10[1])numbers. (10[1])The (10[1])sum along (-5[1])any row (10[2])of (10[1])Pascal’s triangle is (10[1])equal to one (10[1])of (10[2]-5[1])these numbers. (-5[1])These are the (10[1])only integers (10[1])with no odd (-5[2])prime factors. In binary, these numbers consist of (10[2])a one followed by (10[3])all zeros. For (10[2])10 (10[2])points, (10[1])name these numbers which include (10[1]-5[1])4, (10[1]-5[1])8 (10[5]0[1])and (10[3])16, obtained by (10[2]0[2])repeated multiplication by (10[1])the smallest even (10[17]0[8])number. ■END■