Question

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Answer 1

Composite is a number that is NOT prime. So we want to find an odd perfect square that IS prime to be a counterexample.
√36 = Not odd
√49 = 7 Factors only 1 * 7  so it is prime
√81 = 9 Factors 1, 3, 9 composite
√225 = 15 Factors 1,3, 5,9,15, 25, 45, 75, 225 composite

Counterexample for 2∧n - 1 Is prime
2^6 - 1 = 64 - 1 = 63 NOT PRIME Factors are: 1, 3, 7, 9,21, 63
2^5 - 1 = 32 - 1 = 31 Prime
2^3 - 1 = 8 - 1 = 7 Prime
2^2 - 1 = 4 - 1 = 3 Prime