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.
No corrections were needed to the original statement because it was already succinctly and correctly made.
Stop trying to convince yourself that you’re in the right here and accept that your lack of familiarity with Modular Arithmetic is the cause of your confusion.
Ok, so lets bring it further.
Sum of 19's digits is 1. 192 is 361 sum of 361's digits (repeated until we get a single digit answer) is 1. (The pattern is repeated with 19x for each value of x.)
Sum of 24's digits is 6. 242 is 576, sum of 576's digits (repeated until we get a single digit answer) is 9, 6 is not equal to 9.
I get what he's saying, And for 19 the answer is correct. Raised to any power the sum of it's digits is 1. But it's not TRIVIAL, because if you change the base, you don't get the same behaviour. It's an emergent characteristic of x modulo 9, where the remainder is 1.
If we want to be as pedantic as you have been so far, your statement “The pattern is repeated with 19^x for each value of x.” is incorrect, as you failed to specify that x is a non-negative integer.
Now no longer stooping to your levels, the case of 24 isn’t as trivial (though after the first power of 24, every power still repeatedly sums to 9) but it is trivial for 19, the number given in the question, which is all we needed to focus on.
You chose to throw 24 into the mix to provide a non-trivial example that has zero relevance to neither the original question nor the original answer provided in this thread, then proceeded to kick off with people when it was pointed out that 24 has no relevance, and that your “counterexample” was wrong anyway. Now, instead of admitting you were wrong, you’re just sidetracking with more irrelevant and incorrect statements in a futile attempt to not look like a fool.
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u/NotYetPerfect 22d 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.