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.
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$(120)_b = b^2+2b$
$b^2+2b$ can never be a perfect square as $b^2+2b+1$ is (except for $b=0$).
Ian Miller
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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? – Стефан Јовановић Oct 24 '15 at 16:11
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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. – Ian Miller Oct 24 '15 at 16:13