Amicable Pair with Smallest Common Prime Factor 5/Historical Note
Historical Note on Amicable Pair with Smallest Common Prime Factor 5
In $1986$, David Wells reported in his Curious and Interesting Numbers of $1986$ that "numerous mathematicians" had conjectured that all amicable pairs both of whose elements are odd are multiples of $3$.
This amicable pair, a counterexample, was communicated by letter dated $15$th May $1987$ from Herman te Riele to Richard K. Guy.
The latter published it, with mistakes, in his Unsolved Problems in Number Theory, 2nd ed. of $1994$:
- $5 \cdot 7^2 \cdot 11^2 \cdot 13 \cdot 17 \cdot 19^3 \cdot 23 \cdot 37 \cdot 181 \begin{cases} 101 \cdot 8643 \cdot 1947938229 \\ 365147 \cdot 47303071129 \end{cases}$
David Wells repeated the mistakes in his Curious and Interesting Numbers, 2nd ed. of $1997$.
Guy finally published the corrected version in his Unsolved Problems in Number Theory, 3rd ed. of $2004$.
It was for some time believed to be the smallest such amicable pair, but smaller ones have since been discovered.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $220$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $220$