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April 11th, 2012, 11:15 AM  #1 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  A homogeneous variable equation, not so easy!!!
Prove that if F(x+y)=F(x)+F(y) then F(z)=a*z . (Do not involve any types of iteration please, ) Thank you 
April 11th, 2012, 01:13 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,732 Thanks: 689  Re: A homogeneous variable equation, not so easy!!! Quote:
The general idea is to first prove it for y as an integer multiple of x, using mathematical induction. This can then be extended to fractions. To have it hold for reals, you need continuity.  

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