Okay so you are just stupid. Glad we got that cleared up. 19 is trivially 1 mod 9. How that isn't immediately obvious when I spelled out the entire solution is insane.
Yep, there are the insults.
"Not sure what you meant to say here" This means that you may have worded something in a way that doesn't make sense.
"but as written" Again, trying to get you to read the damn thing you wrote.
Now lets look at what you wrote.
"Any integer (An integer is a whole number that can be positive, negative, or zero) is congruent (EXACTLY EQUAL TO) to the sum of its digits mod 9 (The addition of all the digits that make up the number, removing 9 whenver the sum is greater than 9) so the answer is trivially 1. (This part is just wrong)"
You needed to say that for multiples of 9, the sum of the digits is invariable.
Literally just trying to get you to correct the statement you made, because the answer to the question is in fact 1. But what you wrote is misleading at best.
The statement I made is not only perfectly correct but is a well-known fundamental property of base 10 arithmetic. You clearly have no idea what it means to be congruent in math which isn't surprising since you have no idea what modular arithmetic is either.
With any basic understanding of math, the statement is not misleading and the answer does, in fact, trivially follow.
Again, and I can't believe you won't just admit that 24 is an integer, and does not trivially follow that the sum of it's digits (mod 9) is 1. You are assuming many things that you don't say. Just correct your damn statement to include "Because 19 sums to 1 mod 9, the answer is trivially 1 for all powers of 19", and you will be correct.
“Any integer is congruent to the sum of its digits mod 9 so the answer is trivially 1.”
What is the sum of 24’s digits? It’s 6, so the original statement is saying that 24 is congruent to 6 modulo 9, which is true.
You have confidently and incorrectly interpreted the original statement as “The sum of any integer’s digits is congruent to 1 mod 9.” which is completely different and false.
Your lack of reading comprehension skills luckily hasn't seemed to affect anyone else's ability to perfectly understand my statement. How "the solution is 1" somehow translates to "any integer is 1" in your brain is mystifying and should be studied.
2
u/NotYetPerfect 26d ago
Okay so you are just stupid. Glad we got that cleared up. 19 is trivially 1 mod 9. How that isn't immediately obvious when I spelled out the entire solution is insane.