About cookies on this site Our websites require some cookies to function properly (required). In addition, other cookies may be used with your consent to analyze site usage, improve the user experience and for advertising. For more information, please review your options. By visiting our website, you agree to our processing of information as described in IBM’sprivacy statement. To provide a smooth navigation, your cookie preferences will be shared across the IBM web domains listed here.
December 2018 - Solution
Every natural number can be represented as a multiplication of powers of prime numbers.
The exponents of this representation, modulo 2, can be viewed as a linear vector space.
Each “boring” cycle is a linear sub-space, and therefore it is easy to combine two sub-spaces of dimension 3 to a sub-space of dimension 6.
The interesting fact is that one can combine two sets that are *not* linear sub-space together into a linear sub-space.
Many of you found a boring solution with 2,251 solvable numbers, like [[3, 7, 11, 13], [2, 5, 14, 65]].
George Lasry, Deron Stewart, Jingran Lin, Andreas Stiller, Alper Halbutogullari and Oscar Volpatti found solutions with 2,556 solvable numbers such as: [[14, 231, 374, 34], [13, 1482, 95, 10]].
Alper Halbutogullari also found a solution with exactly 2,187 solvable numbers: [[10, 5, 13, 39], [17, 51, 7, 66]].