Tossup

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 these numbers. (-5[4])Every known almost perfect number is one of these numbers. (10[1]-5[12])The cardinality (-5[3])of the power (-5[2])set (-5[1])of any finite (-5[2])set (10[1]-5[3])is one of these numbers. (10[9]-5[10])These (10[1])numbers appear (10[3])in the exponent (10[1])in the formula for Fermat numbers, (10[1])while Mersenne (-5[2])primes (10[1]-5[1])are defined as being one (10[1]-5[1])less (10[5]-5[1])than (10[4])these (10[2]-5[1])numbers. (10[9]-5[4])The (10[1])sum (10[1])along (10[1])any row (-5[1])of Pascal’s (10[2])triangle (10[1])is equal to (10[1])one of these (10[1])numbers. (10[2]-5[1])These are the only integers (10[1])with no (10[1])odd prime factors. (-5[2])In binary, these numbers consist of a one (10[2])followed by all zeros. (10[3])For 10 points, (10[2])name (10[2])these (10[1])numbers which include 4, 8 (10[1]-5[1])and (10[1]-5[1])16, (10[5]0[1])obtained (10[2])by repeated multiplication (10[2]0[2])by the smallest even number. ■END■ (10[17]0[6])

Back to tossups

Buzzes

Summary