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Jan Meyer
2026-04-28 14:27:40 +02:00
parent 4bee68e6c4
commit 35d545c527
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10 Courses/01 - WiSe 2025_26/DAS/Formulas.md
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@@ -29,8 +29,7 @@ Result is the last $"Remainder"$ that is not $0$.
**Goal:** find a $x$ and $y$ so that $"Divident" * x + "Divisor" * y = gcd("Dividend", "Divisor")$
1. **Rewrite Euclid (above) equations** to solve for remainder ($"Remainder" = "Old Remainder" - "Dividend" * "Divisor"$)
2. **Substitute remainders** -> $$
2. **Substitute remainders** ->
## Inclusion-Exclusion Principle
Principle that dictates that when combining / overlapping sets, you have to make sure to not include elements that occur in multiple sets multiple times.
@@ -44,7 +43,7 @@ $$
&15^5 = 759,375 && "--- in the range / below" 10^6 \
&16^5 = 1,048,576 && "--- outside the range / above" 10^6 \
&=> 15 "numbers in the form "x^5"exist" &&
$$
> [!warning]
> Now, we can't add $1,000$ and $15$, since there are numbers that match both, so we need to subtract these duplicates.