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Show that when the square of an odd integer is divided by 4, the remainder is always 1.

 

Let f(x) = x^2 − 2x. Find all real numbers x such that f(x) = f(f(x)).

 Feb 20, 2021
 #1
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If an integer is odd, then it is of the form \(2n+1.\)

 

Square it: \((2n+1)^2 = 4n^2 + 4n +1 = 4(n^2 + n) + 1 \equiv 1 \quad (\mod 4)\)

 

The second question was asked awhile ago: https://web2.0calc.com/questions/plsssss-helppppp-function-question-plssss-its-urgenttt

 Feb 20, 2021

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