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November 24th, 2012, 11:03 PM  #1 
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  find max(n) and m Ans :max(n)=104 , m=2785 
November 24th, 2012, 11:13 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: find max(n) and m
Seems to me m and n are unbounded.

November 24th, 2012, 11:36 PM  #3  
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  Re: find max(n) and m Quote:
but here m and n are natural numbers (the solutions of m and n are limited), we can find max(n) and corresponding m  
November 24th, 2012, 11:44 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: find max(n) and m
D'oh! Yes, my apologies... 
November 25th, 2012, 01:55 AM  #5 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: find max(n) and m
Let and for natural numbers m, k, a. subtract, 2)  1) we want maximum positive integer k therefore we need minimum positive integer a. try a = 1 208 = 2k + 1 impossible try a = 2 208 = 4k + 4 k = 51 m = 51^2 + 184 = 2785 
November 25th, 2012, 02:16 AM  #6 
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  Re: find max(n) and m
excellent 
November 25th, 2012, 03:27 PM  #7 
Senior Member Joined: Apr 2012 Posts: 799 Thanks: 1  Re: find max(n) and m
now please find : min(n) and corresponding m (m and n are also positive integers) Ans:min(n)=26 , m=265 
November 25th, 2012, 04:55 PM  #8 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: find max(n) and m
proceed as before with This time we want the minimum positive integer k wich means we need the maximum positive integer a. a = 14 already makes 1) greater than 208 and odd integers for a have no chance so try a = 12 208 = 24k + 144 impossible for positive integer k try a = 10 208 = 20k + 100 again impossible for positive integer k try a = 8 208 = 16k + 64 k = 9 m = 9^2 + 184 = 265 
November 25th, 2012, 05:29 PM  #9 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: find max(n) and m
....and the inbetween one is: 24, 28, 52 agentredlum = red gunmetal (anagram) 
November 25th, 2012, 06:39 PM  #10  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 233  Re: find max(n) and m Quote:
but i still prefer agent mulder because the character has many qualities i like.  

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