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 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...

View full post »

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...

View full post »

Thread 'Imaginary Pythagoras'

I posted this in the Lame Math thread, but it's got me thinking. Is there any validity to this? Or is it really just a mathematical trick? Naively, I see that i2 + plus 12 does equal zero2. But does this have a meaning? I know one can treat the imaginary number line as just another axis like the reals, but does that mean this does represent a triangle in the complex plane with a hypotenuse of length zero? Ibix offered a rendering of the diagram using what I assume is matrix* notation...

View full post »