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November 24th, 2012, 11:03 PM   #1
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find max(n) and m







Ans :max(n)=104 , m=2785
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November 24th, 2012, 11:13 PM   #2
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Re: find max(n) and m

Seems to me m and n are unbounded.
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November 24th, 2012, 11:36 PM   #3
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Re: find max(n) and m

Quote:
MarkFL wrote :Seems to me m and n are unbounded.
if m and n are positive real numbers then m and n are unbounded

but here m and n are natural numbers (the solutions of m and n are limited), we can find max(n) and corresponding m
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November 24th, 2012, 11:44 PM   #4
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Re: find max(n) and m

D'oh! Yes, my apologies...
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November 25th, 2012, 01:55 AM   #5
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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



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November 25th, 2012, 02:16 AM   #6
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Re: find max(n) and m

excellent
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November 25th, 2012, 03:27 PM   #7
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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
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November 25th, 2012, 04:55 PM   #8
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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



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November 25th, 2012, 05:29 PM   #9
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Re: find max(n) and m

....and the in-between one is: 24, 28, 52

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November 25th, 2012, 06:39 PM   #10
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Re: find max(n) and m

Quote:
Originally Posted by Denis
....and the in-between one is: 24, 28, 52

agentredlum = red gunmetal (anagram)
nice, much better than 'ten drug meal'



but i still prefer agent mulder because the character has many qualities i like.

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