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Question

If n is an even number, then the digit. In the unit place of 22n+1+1 will be ??

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Solution

221221+1=5 ends in 5.

Ifn>1, then 42n and so 15=(241)(22n1).

Hence 22n+12(mod 5), and since 22n+1is odd, we must have 22n+17( mod 10).

Therefore 22n+1 ends in 7 when n>1, and in 5 when n=1.


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