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For how many integers nn where 2≤n≤1002≤n≤100 is (n2)(n2) odd?

 Aug 5, 2018
 #1
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n has to be odd because \(odd^2=odd\)

It cannot be even because \(even^2=even\)

So how many integers from 2 to 100 are odd?

The answer would be 49 integers

 Aug 5, 2018
 #2
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All odd numbers between 3 and 99 will be odd when squared. So, you have:

 

[99 - 3] / 2 + 1 =

96 / 2 + 1          =

48 + 1                = 49 numbers whose squares will be odd. Eamples: 3^2=9, 5^2=25, 7^2=49 and so on.

 Aug 5, 2018

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