statement.html

problem 45 · 20 lines

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<p>Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:</p>
<table><tr><td>Triangle</td>
<td> </td>
<td>$T_n=n(n+1)/2$</td>
<td> </td>
<td>$1, 3, 6, 10, 15, \dots$</td>
</tr><tr><td>Pentagonal</td>
<td> </td>
<td>$P_n=n(3n - 1)/2$</td>
<td> </td>
<td>$1, 5, 12, 22, 35, \dots$</td>
</tr><tr><td>Hexagonal</td>
<td> </td>
<td>$H_n=n(2n - 1)$</td>
<td> </td>
<td>$1, 6, 15, 28, 45, \dots$</td>
</tr></table><p>It can be verified that $T_{285} = P_{165} = H_{143} = 40755$.</p>
<p>Find the next triangle number that is also pentagonal and hexagonal.</p>
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