MHB How to Find the Remainder of a Modulo Operation in Factorial Series?

  • Thread starter Thread starter Albert1
  • Start date Start date
AI Thread Summary
The discussion focuses on calculating the sum \( A = \sum_{k=1}^{91}(k! \times k) \) and finding \( A \mod 2002 \). A key observation is the simplification of \( k! \times k \) to \( (k+1)! - k! \). Participants note a typo in the original expression, which is acknowledged and corrected. The conversation highlights the importance of accuracy in mathematical expressions, especially when using mobile devices for posting. Overall, the thread emphasizes the process of modular arithmetic in factorial series.
Albert1
Messages
1,221
Reaction score
0
$A=\sum_{k=1}^{91}(k!\times k)$

find $ A $ MOD 2002
 
Mathematics news on Phys.org
Since $k!k = k! ((k+1)-1) = (k+1)! - k!$ for all $k$, $A$ telescopes to 92! - 1. Since $2002 = 2 \cdot 7 \cdot 11 \cdot 13$, $92!$ is divisible by 2002 and hence $A = 2001 \pmod{2002}$.
 
Last edited:
Euge said:
Since $k!k = k! ((k+1)-1) = (k+1)! - k$ for all $k$, $A$ telescopes to 92! - 1. Since $2002 = 2 \cdot 7 \cdot 11 \cdot 13$, $92!$ is divisible by 2002 and hence $A = 2001 \pmod{2002}$.
very nice !
a typo :$k!k=k!(k+1-1)=(k+1)!-k!$
 
Albert said:
very nice !
a typo :$k!k=k!(k+1-1)=(k+1)!-k!$

Thanks. I use my phone to post answers here, and sometimes the keyboard doesn't function properly. I will make the correction.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Back
Top