Smallest Solution to Equation p^p times q^q = r^r

Theorem

Consider the Diophantine equation:

$p^p \times q^q = r^r$

Its smallest solution is:

\(\ds p\)

\(=\)

\(\ds 12^6\)

\(\ds = 2 \, 985 \, 984\)

\(\ds q\)

\(=\)

\(\ds 6^8\)

\(\ds = 1 \, 679 \, 616\)

\(\ds r\)

\(=\)

\(\ds 2^{11} \times 3^7\)

\(\ds = 4 \, 478 \, 976\)

Proof

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Sources

• 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $4,478,976$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $4,478,976$