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August 26th, 2012, 10:26 PM  #1 
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  The last two digits Ans:28 
August 27th, 2012, 09:42 AM  #2 
Senior Member Joined: Jun 2011 Posts: 164 Thanks: 0  Re: The last two digits
I just saw this problem, have not thought about it yet, but I will give it try right here: if we just replace n with m, we get: (2^(4m+2))(2^(4m+3)1) and we know m is a multiple of 0.5 that is greater or equal to 0 because that is the only way n will be a natural number now if we set 4m+2=2n=x, therefore 4m+3=x+1 we have 2^x(2^(x+1)1) =(2^x)(2^x*21) since n is a natural number, x must be a natural number that is even so: 2^2*(2^31)=28 2^4*(2^51)=496 2^6*(2^71)=8128 2^8(2^91)=130816 2^10(2^111)=...28 I have a question now, when n=2, the last two digits are 96, could you please check your problem? Or did I do something wrong? 
August 27th, 2012, 05:01 PM  #3 
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  Re: The last two digits
wuzhe : so n is an odd number, not even numbers 
August 27th, 2012, 06:15 PM  #4 
Senior Member Joined: Jun 2011 Posts: 164 Thanks: 0  Re: The last two digits
But I thought m could be 0.5 or 1.5, did I miss something basic?

August 27th, 2012, 06:58 PM  #5  
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  Re: The last two digits Quote:
I have edited the original post  
August 27th, 2012, 07:02 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: The last two digits
If m is to be a nonnegative integer, then you could use or . is used to denote the integers. is used to denote the natural numbers. is used to denote the natural numbers and includes zero as well, i.e., the whole numbers. 
August 27th, 2012, 07:06 PM  #7 
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  Re: The last two digits
MarkFL : Thanks 
August 27th, 2012, 07:30 PM  #8 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: The last two digits
Another offtopic suggestion: To use to display text, use the text command: The code \text{ your text here } produces This way, your text is not italicized like variables. 
August 27th, 2012, 07:39 PM  #9 
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  Re: The last two digits
Hint :to prove this, one of the possible solutions you may use Mathematical Induction (MI), please try it I will post using another method later. 

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