



 
Ashish, we have three responses for you. Ashish, I'll show you for n = 2 and you can do the general situation. Suppose that your integer is k then you can write
where p is an integer and q and r are digits. For example 25654 = 25600 + 50 + 4 = 25600 + 54. Since p * 100 is divisible by 2^{2 } = 4, k is divisible by 2^{2 } if and only if q * 10 + r is divisible by 2^{2 }. I hope this helps,
In our March Problem of the Month this year, you find the following argument:
Claude.
Another example: What you need to think about is the part of the number appearing
before the last n digits. Look at 35640 for example. This means 35 x
1000 + 640 = 35 x 10^{3 } + 640. What do you know about 2^{3 } dividing
10^{3 }?  


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