This conjecture states that all the solutions to \\(\\ell _1!\\cdots \\ell _m!=k!\\) with \\(k-\\ell _m\\ge 2\\) are \\((\\ell _1,\\ldots ,\\ell _m;k)=(6,7;10),(3,5,7;10),(2,5,14;16)\\) and (2,3,3,7;9). In this paper, we generalize the ...
Ifa is not divisible byp, Fermat's little theorem is equivalent to the statement thatap− 1− 1 is an integer multiple ofp, or in symbols For example, ifa = 2 andp = 7 then 26= 64 and 64 − 1 = 63 is thus a multiple of 7. 我们设 x = N!,那么由费马小定理:x * (n+...
There are some numbers which can be expressed by the sum of factorials. For example 9, 9 = 1! + 2! + 3! . Dr. von Neumann was very interested in such numbers. So, he gives you a number n, and wants you to tell whether or not the number can be expressed by the sum of some...
The main purpose of this paper is to emphasize the role of a CAS as an experimental tool that students might use to formulate conjectures regarding the digits of n!.doi:10.2307/2687088Treuden Michael L.Mathematical Association of AmericaCollege Mathematics Journal...
Well, it’s just a piece of cake. For a given n, you’ll check if there are some xi, and let n equal to Σ1<=i<=txi!. (t >=1 1, xi >= 0, xi = xj iff. i = j). If the answer is yes, say “YES”; otherwise, print out “NO”. ...