MHB Divisibility of (1!+2!+3!+...+100!)^2 by 5

Thread starter stamenkovoca02
Start date Mar 17, 2021
Tags

Divisibility

AI Thread Summary

The discussion centers on determining the remainder of (1!+2!+3!+...+100!)^2 when divided by 5. It is noted that 5 divides evenly into factorials starting from 5! and higher, while lower factorials like 4! and 3! do not contribute to divisibility by 5. The impact of squaring the sum on the overall divisibility is questioned. Participants are encouraged to explore the problem further rather than seeking a direct answer. The conversation emphasizes the importance of understanding factorial properties in relation to divisibility.

Mar 17, 2021

stamenkovoca02

1.The remainder when dividing (1!+2!+3!+...+100!)^2 by 5 is?
5 divides evenly into 5!, 6!, 7!, ..., 100!. It would also divide evenly into things like 2!*8! or 20!*83!, but not 4!*3!
but whether then ^2 affects the rest?
And what is answer?Thanks

Mathematics news on Phys.org

Mar 17, 2021

cbarker1

Gold Member

MHB

You have to show some type of attempt. We can't provide the answer, but we can guide you to the answer.

Thread 'Non-orthogonal bases'

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...

View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...

View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

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...

View full post »