P851
projecteuler.net

SOP and POS

ℹ️Published on Sunday, 9th July 2023, 11:00 am; Solved by 151;
Difficulty rating: 85%

Let n be a positive integer and let En be the set of n-tuples of strictly positive integers.

For u=(u1,,un) and v=(v1,,vn) two elements of En, we define:

  • the Sum Of Products of u and v, denoted by u,v, as the sum i=1nuivi;
  • the Product Of Sums of u and v, denoted by uv, as the product i=1n(ui+vi).

Let Rn(M) be the sum of uv over all ordered pairs (u,v) in En such that u,v=M.
For example: R1(10)=36, R2(100)=1873044, R2(100!)446575636mod109+7.

Find R6(10000!). Give your answer modulo 109+7.



Soluzione

Last modified: June 14, 2025. Website built with Franklin.jl and the lovely Julia programming language.