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April 6th, 2014, 01:05 PM   #1
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m and n

2^m .5^n +2^3+5^n=101
find m+n
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April 6th, 2014, 01:36 PM   #2
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Do you mean $2^m5^n+2^\color{red}m+5^n=101$?
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April 6th, 2014, 05:09 PM   #3
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Originally Posted by mared View Post
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.
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April 14th, 2014, 05:16 AM   #4
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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 $

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