statement.html

problem 29 · 12 lines

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<p>Consider all integer combinations of $a^b$ for $2 \le a \le 5$ and $2 \le b \le 5$:
$$\begin{array}{rrrr}
2^2=4, &amp;2^3=8, &amp;2^4=16, &amp;2^5=32\\
3^2=9, &amp;3^3=27, &amp;3^4=81, &amp;3^5=243\\
4^2=16, &amp;4^3=64, &amp;4^4=256, &amp;4^5=1024\\
5^2=25, &amp;5^3=125, &amp;5^4=625, &amp;5^5=3125
\end{array}$$</p>
<p>If they are then placed in numerical order, with any repeats removed, we get the following sequence of $15$ distinct terms:
$$4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125.$$</p>
<p>How many distinct terms are in the sequence generated by $a^b$ for $2 \le a \le 100$ and $2 \le b \le 100$?</p>
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