Tetramagic square, 256th order

Charles Devimeux in 1981 (Brest 1919 - Lestrevet Plomodiern 2000), and a HP 41CV

The first tetramagic square, at that time called quadrimagic, was constructed by Charles Devimeux and announced in the November 1983 issue of La Jaune et La Rouge, the monthly magazine published by the Société Amicale des Anciens Elèves de l'Ecole Polytechnique. He computed his 256th-order square using a HP 41CV, a programmable pocket calculator, and printed it in an "atlas" of 64 pages, using a HP 82143A printer. The atlas listing the square being too big (256x256 means 65536 numbers...) and the foreseen note by Devimeux explaining his method being not yet available (and anyway would have been too long), they were not published. And unfortunately it seems that they are definitely lost: even if one copy of the atlas was said to have been received by the Société Amicale and even if the readers of the magazine could ask copies of the future note, we were unable to locate any copy of them in spite of our best efforts. See the thanks at the end of this page.

Fortunately La Jaune et La Rouge briefly mentionned the construction method used, before the availibility of the note foreseen by Devimeux. Even if the method was not enough detailed to be directly used, we can recognize the Tarry-Cazalas method. Using the row keys (7555, 15041, 29920, 59504, 53560, 41756, 18190, 36359), column keys (7352, 14428, 28718, 57367, 49547, 33733, 2018, 3697) and the additive key 3 given in the magazine, I was very happy to compute and verify his square more than 20 years later: I can now confirm that his square was really tetramagic! Here is his square:

• Devimeux's tetramagic square (zipped Excel file, 276Kb). Its multimagic sums are:
• S1  = 8388480
• S2  = 366495487360
• S3  = 18013848757862400
• S4  = 944437268143413954688

However, bad news for me: all this means the Boyer-Viricel tetramagic 512 (in 2001) and Boyer tetramagic 256 (in 2003) squares can no longer be considered as the first known tetramagic squares records! Hopefully, the Boyer-Viricel pentamagic 1024 (in 2001) square still seems to be the first constructed pentamagic square...

A supplemental information. Pierre Tougne had received a letter from Charles Devimeux dated November 8th 1984 saying that he had constructed a tetramagic square during "nearly two years", a letter in which he gave exactly the same keys than above. Information very briefly mentioned, but this time without the keys, at the end of the Pierre Tougne's "Jeux Mathématiques" column in Pour La Science, April 1985, page 100.

For more details:

 Particular thanks: Francis Gaspalou who discovered this forgotten paper of 1983, revealing the Devimeux square. Claudine Billoux who tried -without success- to find the Devimeux atlas in the La Jaune et La Rouge archives owned by the Ecole Polytechnique library. Annick Devimeux who tried -also without success- to find the atlas and note of her husband. Pierre Tougne for the information on his Pour La Science paper and on the Devimeux's letter. Jean Moreau de Saint-Martin who published my advertisement in his column, even if unfortunately nobody answered that he had a copy of the Devimeux atlas or note.