Smallest Integer which is Product of 4 Triples all with Same Sum/Historical Note

Historical Note on Smallest Integer which is Product of 4 Triples all with Same Sum

Richard K. Guy discusses this result in his Unsolved Problems in Number Theory of $1981$, and carries it forward into later editions.

In his Unsolved Problems in Number Theory, 3rd ed. of $2004$, the result is presented as:

It may be of interest to ask for the smallest sums or products with each multiplicity. For example, for $4$ triples, J. G. Mauldon finds the smallest common sum to be $118$ ... and the smallest common product to be $25200$ ...

However, in the article cited by Richard K. Guy, which appears in American Mathematical Monthly for Feb. $1981$, in fact J. G. Mauldon does no such thing.

Instead, he raises the question for $5$ such triples.

David Wells, in his Curious and Interesting Numbers, 2nd ed. of $1997$, propagates this, accrediting the result to Mauldron, citing that same problem in American Mathematical Monthly.

It is also apparent that Mauldron is a misprint for J.G. Mauldon.

Sources

• Feb. 1981: J.G. Mauldon: Elementary Problems: E2872 (Amer. Math. Monthly Vol. 88, no. 2: p. 148)  www.jstor.org/stable/2321140

• Sep. 1982: Lorraine L. Foster and Gabriel Robins: E2872 (Amer. Math. Monthly Vol. 89, no. 7: pp. 499 – 500)  www.jstor.org/stable/2321396

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $25,200$
• 2004: Richard K. Guy: Unsolved Problems in Number Theory (3rd ed.): $\text D 16$: Triples with the same sum and same product