spoon737
spoon737
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Since you are reading up on abstract algebra, I'm assuming you know what the ring axioms are. Let a be an element of any ring. Then, by definition, -a is the additive inverse of a (the unique element with the property that a + (-a) = -a + a = 0). …
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Let b be your base. Then 32+135=211 means (3b + 2) + (b^2 + 3b + 5) = 2b^2 + b + 1 which simplifies to 0 = b^2 - 5b - 6 0 = (b+1)(b-6) So, b is either -1 or 6. However, a negative number base makes no sense, so your base must be 6.
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Let b be your base. Then 32+135=211 means (3b + 2) + (b^2 + 3b + 5) = 2b^2 + b + 1 which simplifies to 0 = b^2 - 5b - 6 0 = (b+1)(b-6) So, b is either -1 or 6. However, a negative number base makes no sense, so your base must be 6.