Question

Q. Show that a perfect square never leaves remainder 2 on dividing by 3. ​

Answer 1

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Answer 2

With that, we have successfully shown that there is no square number that leaves the remainder 2 after being divided by 3. therefore an ² = 3+2 has no preimage ∈︎ℤ mapping to it by , therefore no such ² terms exist. All integers not divisible by 3 can be written as 3m1.

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