Counting is Not an Easy Task

For any prime number P P , let A P A_{P} be the set of integers d { 1 , 2 , 3 , 999 } d \in \{1, 2, 3, \cdots 999\} such that the power of P P in the prime factorization of d d is odd. Then the Cardinality of

1: A 3 A_{3} is 250

2: A 5 A_{5} is 160

3: A 7 A_{7} is 124

4: A 11 A_{11} is 82

Which of the above Statements is False ?

4 All are Correct 2 1 3

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