Australian Mathematics Competition Junior last question

Number Theory Level 4

I just took AMC (Australian Mathematics Competition) Junior and unfortunately, I got the last question wrong. I was left with a few minutes to do the question and found a suitable answer but was not the largest. Here's the question essentially:

Find the largest number that fits the following criteria

\(\overline { abc } =a+{ b }^{ 2 }+{ c }^{ 3 }\)

For example, 135 (which was my answer) fits the criteria.


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