Theorem of Even Perfect Numbers/Necessary Condition/Historical Note

Historical Note on Theorem of Even Perfect Numbers

René Descartes stated in $1638$ that he had a proof that every even perfect number is of the form $2^{p - 1} \paren {2^p - 1}$, but failed to actually produce it.

The first actual published proof was made by Leonhard Paul Euler.

Sources

• 1919: Leonard Eugene Dickson: History of the Theory of Numbers: Volume $\text { I }$ ... (previous) ... (next): Preface
• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $28$
• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.2$: More about Numbers: Irrationals, Perfect Numbers and Mersenne Primes
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $28$