Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Inductive Proof (+linear equation in four variables)

  1. Sep 21, 2011 #1
    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.
  2. jcsd
  3. Sep 22, 2011 #2


    User Avatar
    Science Advisor
    Homework Helper

    If you have to add one to a number, how could you do that if you only have increments / decrements of 2 and 3 available?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Inductive Proof (+linear equation in four variables)
  1. Proof by Induction (Replies: 7)

  2. Induction Proof (Replies: 4)

  3. Linear Proofs (Replies: 4)

  4. Proof by induction (Replies: 4)