Find a and b in the equation
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Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
$3^a - 7^b -1 = 0$ find the value of a and b in integer?
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HandaramTheGreat
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Re: Find a and b in the equation
$3^a-7^b=1$
unit digits of any power of $3$ are always $3$, $9$, $7$ and $1$ ... and same of any power of $7$ are always $7$, $9$, $3$, $1$... so, the difference of $3^a$ and $7^b$ can never be $1$...
no solution...
unit digits of any power of $3$ are always $3$, $9$, $7$ and $1$ ... and same of any power of $7$ are always $7$, $9$, $3$, $1$... so, the difference of $3^a$ and $7^b$ can never be $1$...
no solution...
Re: Find a and b in the equation
observe that ... $a>b$
and $3^a=$odd integer
$7^b=$odd integer
so; odd integer $-$odd integer=even integer .
this contradicts with the given equation .
so no solution
and $3^a=$odd integer
$7^b=$odd integer
so; odd integer $-$odd integer=even integer .
this contradicts with the given equation .
so no solution