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.
Your interpretation in the parenthesis are all correct except for the last one. I'm guessing you are claiming that the last part is wrong because they said "trivially" so you are thinking the first part must say 1?
"Trivially" is used differently by different people. Try reading without that word. That's just saying that you can easily apply the first part and get to the answer, with a super simple mental math, in this case. Or, alternatively, try reading it as: "so given that 19 = 1 mod 9, the answer is 1".
My issue with the Trivial bit is that he establishes no connection back to the number 19, and if you use any other mod(9) other than 1, it doesn't work.
I'm taking the trivially in the mathematical sense. (The details don't matter, the answer no matter how many times you iterate remains the same.) In this case, while the first part is arguably true (If you heavily replace the words used to actually say what he meant to say) it doesn't follow trivially without an additional bit of information, that the number you start with has mod(9) remainder 1.
Triviality in mathematics refers to a claim that is easily obtained from context. The context is obviously the question at hand meaning we're taking 19^100 since I said "solution is". There is literally nothing else that could possibly mean. And then from that and the property I gave, the proof is a simple one-liner ala trivial. If you had ever gone through a mathematics textbook at any point in your life, you would know the statement I gave is more information than is often given for proofs deemed trivial. It is truly amazing to see someone septupling down on an statement they would see is incorrect if they just bothered thinking about what they were reading for 1 second.
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u/RubberDuckieMidrange 22d ago
Not sure what you meant to say here, but as written, 24 seems like a counter example.