If you take any single number and multiple by 10, you get a double digit number that ends in 0. Eg, 7*10=70 How do you prove that any single number added 10 times always ends up with a zero in its last digit? And a stronger lemma: any number added 10 times ends up with 0 in its last digit. Please only answers from quants from citadel, Jane street, 2 sigma or model researches from open ai or Google or anthropic , in order to keep the answer quality high. Thanks 🙏🙏
Base Case: 1 added 10 times ends in 0. Trivially true. Assume for the sake of induction that a number n added 10 times ends in 0. Now, consider adding n+1 together 10 times. This is equivalent to adding n ten times + adding one ten times = adding n ten times + 10. Since we know adding n ten times ends in a 0 (by assumption) and adding two numbers that end in 0 always ends in 0 (I guess we could also prove this if you feel it necessary, but it’s trivial), summing n+1 ten times ends in 0. Thus our induction is complete and any number >=1 added together 10 times will end in 0. You can prove it for all integers too, it’s no different. Induction is dope.
What kind of dumbass question is this? Anyone that took algebra and paid a modicum of attention would be able to prove this with induction.
Ah yes quite simple. I will leave the proof as an exercise for the reader :)
I’m commenting just to represent citadel
Didn’t even read the question. Just want to represent CitSec here
I'm disappointed that my peers are doing someone's high school math homework on Blind.
LMAO what the hell
“Stronger” lemma 🤣 ok, sunshine, do you want us to start at Peano postulates?
10=0 (mod 10), hence 10x=0x (mod 10)
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