I got this problem i need to solve: At what base b, where b>2 , (120)b equals x2, where x is in decimal number system? I need to find all bases b, and i need to see the process of finding answer, so i can do it myself.

  • 4
    $\begingroup$ Hint: $(120)_b=b^2+2b=(b+1)^2-1$. $\endgroup$ – Apple Oct 24 '15 at 16:05

$(120)_b = b^2+2b$

$b^2+2b$ can never be a perfect square as $b^2+2b+1$ is (except for $b=0$).

  • $\begingroup$ That is what i thought as well, but can that be presented as valid proof, or do i need to find other way to prove it? $\endgroup$ – Стефан Јовановић Oct 24 '15 at 16:11
  • $\begingroup$ Yes. Or include Apple's hint and express it as $(b+1)^2-1$ to show that it is always one less than a perfect square. $\endgroup$ – Ian Miller Oct 24 '15 at 16:13

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.