Henry Ernest Dudeney/Puzzles and Curious Problems/159 - The Year 1927

Puzzles and Curious Problems by Henry Ernest Dudeney: $159$

The Year $1927$

Can you find values for $p$ and $q$ such that $p^q - q^p = 1927$?

To make it perfectly clear, we will give an example for the year $1844$, where $p = 3$ and $q = 7$:

$3^7 - 7^3 = 1844$

Can you express $1927$ in the same curious way?

Sources

• 1932: Henry Ernest Dudeney: Puzzles and Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Various Arithmetical and Algebraical Problems: $159$. -- The Year $1927$
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Arithmetical and Algebraical Problems: Miscellaneous Puzzles: $226$. The Year $1927$