I'm trying to prove by induction that [tex]\forall n \geq 5, \exists m_1, m_2 \in \mathbb{N} [/tex] such that [tex] n = 2m_1 +3m_2. [/tex]I've done the base case, and the inductive step boils down to showing that [tex] \exists m_1 \prime m_2 \prime [/tex] such that [tex]2m_1 +3m_2 +1 = 2m_1 \prime +3m_2 \prime [/tex]. Maybe I'm forgetting something from grade school algebra, but I have no idea how to solve for [tex] m_1 \prime, m_2 \prime [/tex]. I've plugged it into wolfram alpha [http://www.wolframalpha.com/input/?i=2*x_1+3*x_2+++1+=+2*y_1+++3*y_2] and got solutions (all I care about is the case n =1 for the integer solutions wolfram gives) but I want to know how to arrive there.(adsbygoogle = window.adsbygoogle || []).push({});

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Inductive Proof (+linear equation in four variables)

Loading...

Similar Threads for Inductive Proof +linear |
---|

A Is the proof of these results correct? |

I Doubt about proof on self-adjoint operators. |

I Addition of exponents proof in group theory |

B Help understanding a proof |

**Physics Forums | Science Articles, Homework Help, Discussion**