Hello Math-Fun, The ideas expressed in my former mail came from three sources: — Werner Keym's (wonderful) last book: https://chesscafe.com/book-reviews/chess-problems-out-of-the-box-by-werner-k... — This recent video by Numberphile on YouTube (april 2020): https://www.youtube.com/watch?v=xyVl-tcB8pI&feature=youtu.be — This sequence of the OEIS ("numbers that are the sum of two squares"): 0, 1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18, 20, 25, 26, 29, 32, 34, 36, 37, 40, 41, 45, 49, 50, 52, 53, 58, 61, 64, 65, 68, 72, 73, 74, 80, 81, 82, 85, 89, 90, 97, 98, 100, 101, 104, 106, 109, 113, 116, 117, 121, 122, 125, 128, 130, 136, 137, 144, 145, 146, 148, 149, 153, 157, 160,... — Updates of my page will be there: http://cinquantesignes.blogspot.com/2020/06/prime-squares.html Best, É.
Le 30 juin 2020 à 02:54, Éric Angelini <bk263401@skynet.be> a écrit : Hello Math-Fun, today we'll look for « prime squares » and square squares.
Definition 1 A "prime square" is a prime which is the sum of 4 integers. Those integers must occupy the 4 vertices of a geometric square formed formed by 4 cell-centers properly chosen on an infinite grid (...) +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | 1 | 3 | 6 | 10| 15| 21| 28| 36| 45| 55| 66| 78| 91|105|120| | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | 2 | 5 | 9 | 14| 20| 27| 35| 44| 54| 65| 77| 90|104|119| | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | 4 | 8 | 12| 19| 26| 34| 43| 53| 64| 76| 89|103|118| | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | 7 | 12| 18| 25| 33| 42| 52| 63| 75| 88|102|117| | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | 11| 17| 24| 32| 41| 51| 62| 74| 87|101|116| | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | 16| 23| 31| 40| 50| 61| 73| 86|100|115| | | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | 22| 30| 39| 49| 60| 72| 85| 99|114| | | | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | 29| 38| 48| 59| 71| 84| 98|113| | | | | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | 37| 47| 58| 70| 83| 97|112| | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | 46| 57| 69| 82| 96|111| | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | 56| 68| 81| 95|110| | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | 67| 80| 94|109| | | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | 79| 93|108| | | | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | 92|107| | | | | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ |106| | | | | | | | | | | | | | | | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+ (...)