Proof by induction! Urgh! :(

**Jimbobobo** · November 20th 2007, 02:13 PM

edit
11^2 + 12^1 = 133
11n+3 + 12^2n+3
But then I get stuck!? Any ideas?

**Plato** · November 20th 2007, 02:42 PM

Say it is true for K>1, $\left( {11} \right)^{K + 2} + \left( {12} \right)^{2K + 1} = 133j$ .
Look at the case of K+1.
$\left( {11} \right)^{\left( {K + 1} \right) + 2} + \left( {12} \right)^{2\left( {K + 1} \right) + 1}$
$= \left( {11} \right)^{K + 3} + 11\left( {12} \right)^{2K + 1} - 11\left( {12} \right)^{2K + 1} + \left( {12} \right)^{2K + 3}$
$\begin{array}{l}<br /> = 11\left[ {\left( {11} \right)^{K + 2} + \left( {12} \right)^{2K + 1} } \right] + \left( {12} \right)^{2K + 1} \left[ { - 11 + \left( {12} \right)^2 } \right] \\ <br /> = 11\left[ {133j} \right] + \left( {12} \right)^{2K + 1} \left[ {133} \right] \\ <br /> \end{array}<br />$

**topsquark** · November 21st 2007, 08:30 AM

Plato either wins the award for most psychic Math Helper, or Jimbobobo edited his original question to the point where it is meaningless. I'm curious as to which?

-Dan

**Plato** · November 21st 2007, 08:43 AM

The original question was edited.

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