First of all, the modular inverse of n modulo k can only exist if GCD(n, k) = 1.
We have
130 = 2 • 5 • 13
231 = 3 • 7 • 11
so n must be free of 2, 3, 5, 7, 11, and 13, which are the first six primes. It follows that n = 17 must the least integer that satisfies the conditions.
To verify the claim, we try to solve the system of congruences
Use the Euclidean algorithm to express 1 as a linear combination of 130 and 17:
130 = 7 • 17 + 11
17 = 1 • 11 + 6
11 = 1 • 6 + 5
6 = 1 • 5 + 1
⇒ 1 = 23 • 17 - 3 • 130
Then
23 • 17 - 3 • 130 ≡ 23 • 17 ≡ 1 (mod 130)
so that x = 23.
Repeat for 231 and 17:
231 = 13 • 17 + 10
17 = 1 • 10 + 7
10 = 1 • 7 + 3
7 = 2 • 3 + 1
⇒ 1 = 68 • 17 - 5 • 231
Then
68 • 17 - 5 • 231 ≡ = 68 • 17 ≡ 1 (mod 231)
so that y = 68.
4.9 then divide by .7 and you get 7 then 7x3=21
So, 21 Amoeba Proteus would be lined up to equal 3 Pelomyxa Palustris.
Algebra cab act as a tool to improve communication by showing specific patterns and possible connections.
<h3>How to illustrate the information?</h3>
Algebra is a symbol that's used to represent mathematical connections. It's a tool that people may and do use to model and answer questions about real-life scenarios.
It should be noted that much of arithmetic operations are typically given out using algebra, as this is a language of specific patterns and possible connections.
It is also a means of working with abstract notions and then applying them, which frequently leads to the formation of generalizations and insights outside of the original context.
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