Triangular Number cannot be Fifth Power

Theorem

Let $T_n$ be the $n$th triangular number such that $n > 1$.

Then $T_n$ cannot be the $5$th power of an integer.

Proof

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Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $15$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $15$