G
Guest
Guest
What is the least positive interger n such that 3n - n3 is an even 4 digit #.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an alternative browser.
You should upgrade or use an alternative browser.
Hello, Ashley Cook!
First of all, I'll take a flying guess at what you meant . . .
\(\displaystyle \;\;\)(Edit: I see that Gene is on the same wavelength.)
\(\displaystyle \;\;\)Graphing? \(\displaystyle \;\)modulo artihmetic? \(\displaystyle \;\) trial-and-error?
I noted that \(\displaystyle 3^n\) is an odd number\(\displaystyle \;\;\Rightarrow\;\;n^3\) must be odd\(\displaystyle \;\;\Rightarrow\;\;n\) is odd.
Then try: \(\displaystyle \,n\:=\:1,\,3,\,5,\,7,\,\cdots\)
First of all, I'll take a flying guess at what you meant . . .
\(\displaystyle \;\;\)(Edit: I see that Gene is on the same wavelength.)
Second, what techniques are available to you?What is the least positive interger \(\displaystyle n\) such that \(\displaystyle \,3^n\,-\,n^3\) is an even 4-digit number.
\(\displaystyle \;\;\)Graphing? \(\displaystyle \;\)modulo artihmetic? \(\displaystyle \;\) trial-and-error?
I noted that \(\displaystyle 3^n\) is an odd number\(\displaystyle \;\;\Rightarrow\;\;n^3\) must be odd\(\displaystyle \;\;\Rightarrow\;\;n\) is odd.
Then try: \(\displaystyle \,n\:=\:1,\,3,\,5,\,7,\,\cdots\)