Question 1042857: a, b, n ∈ Z with n > 1. Prove that if a ≡ b (mod n) then 2a ≡ 2b (mod n).
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! a congruent to b modulus n means that a-b is divisible by n
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then we have
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a - b = nc where c is an integer
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then we have
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a = b + nc
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multiply both sides of the = by 2
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2a = 2b + 2nc
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we have a, b, n, c are integers, then
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2c is an integer say p, then
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2a = 2b + np = 2b mod n
We are done
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