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Statement 1: Remainder when 3456^2222 is...

Statement 1: Remainder when `3456^2222` is divided by 7 is 4. Statement 2: Remainder when`5^2222` is divided by 7 is 4.

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Verified by Experts

The correct Answer is:
4
`3456^(2222) = (7xx493+5)^(2222)`
`= (7k+5)^(2222)`
`= 7m + 5^(2222)`
Now, `5^(2222) = 5^(2)(5^(3))^(740)`
`= 25(125)^(740)`
`= 25(126-1)^(740)`
`= 25[7n+1]`
`= 175n+ 25` ltbRgt Remainder when `175n + 25 ` is divided by 7 is 4.
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