Round 5: Tossup 6

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

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