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 April 6th, 2014, 01:05 PM #1 Senior Member   Joined: Nov 2013 Posts: 434 Thanks: 8 m and n 2^m .5^n +2^3+5^n=101 find m+n April 6th, 2014, 01:36 PM #2 Senior Member   Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra Do you mean $2^m5^n+2^\color{red}m+5^n=101$? April 6th, 2014, 05:09 PM   #3
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Quote:
 Originally Posted by mared 2^m .5^n +2^3+5^n=101 find m+n
Mared, you were asked before to please be clear.
Once more: please be clear. April 14th, 2014, 05:16 AM #4 Senior Member   Joined: Jul 2013 From: Croatia Posts: 180 Thanks: 11 If he really meant $\displaystyle 2^m \cdot 5^n+2^m+5^n=101$ $\displaystyle 2^m=x$ $\displaystyle 5^n=y$ $\displaystyle xy+x+y=101$ $\displaystyle xy+x+y+1=102$ $\displaystyle (x+1)(y+1)=102=51 \cdot 2=34 \cdot 3 =17 \cdot 6$ ; x+1 is always odd and y+1 is always even the only integer solution is when $\displaystyle 2^m+1=17 \Rightarrow m=4$ $\displaystyle 5^n+1=6 \Rightarrow n=1$ m+n=5 Thanks from Olinguito Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode

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