From the proof of modular congruence below, it has been shown that;
41 ≡ 21 (mod 3).
How to Solve Modular Arithmetic?
We want to use the definition of modular congruence to prove that;
41 is congruent to 21 (mod 3) i.e if a ≡ b (mod m) then b ≡ a (mod m).
We are trying to prove that modular congruence mod 3 is a symmetric relation on the integers.
First, if we recall the definition of modular congruence:
For integers a, b and positive integer m,
a ≡ b (mod m) if and only if m|a–b
Suppose 41 ≡ 21 (mod 3).
Then, by definition, 3|41–21, so there is an integer k such that 41 – 21 = 3k.
Thus;
–(41 – 21) = –3k
So
21 – 41 = 3(–k)
This shows that 3|21 – 41.
Thus;
21 ≡ 41 (mod 3) and the proof is complete
Read more about Modular Arithmetic at; https://brainly.com/question/16032865
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