Given the following quadratic equation: \(\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}-{3}{x}-{1}\) For \(\displaystyle{x},{1}\leq{\left\lbrace{x}\right\rbrace}\leq{\left\lbrace{100}\right\rbrace},{x}\equiv{1}\text{mod}{2}\) Is

Amya Horn

Amya Horn

Answered question

2022-03-25

Given the following quadratic equation:
f(x)=x23x1
For x,1x100,x1mod2
Is this true for all x? If so, is there a way to prove it?

Answer & Explanation

Rachettolyf8

Rachettolyf8

Beginner2022-03-26Added 9 answers

Step 1
If x=2k+1, then
x23k1
=(2k+1)23(2k+1)1
=2k(2k1)31±mod2,
so the result is always odd.

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