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Post by ABC Singh on Oct 25, 2014 17:14:07 GMT 5.5
Sir/Madam,
I confuse this question,please help me
" If a,b are natural numbers such that 2013 + a2 = b2, then find the minimum possible value of ab."
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Post by Thoithoi O'Cottage on Oct 25, 2014 19:56:19 GMT 5.5
Hmmm... Though I wholeheartedly love mathematics, I am really disinclined to fancy participating in and contributing to a mathematics discussion simply because I am not worthy. Honestly. However, in the absence of enough people right for this category, I am responding just to encourage discussions here generally. In fact, I have conducted a quick online research on the question but for which I would not have been able to respond at all.
Here it is:
The smallest possible values of a and b are 14 and 47, respectively. Thus, the smallest possible value of ab is
14 × 47 = 658.
That is to say
2013 + a2 = b2
=> 2013 + (14 × 14) = (47 × 47)
=> 2209 = 2209.
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Post by Thoithoi O'Cottage on Oct 25, 2014 20:26:57 GMT 5.5
Here is the calculation:
(b -- a) (b + a) = 2013 = 3 × 11 × 61
ab is minimum when b -- a = 33
and b + a = 61
Here,
a = 14
b = 4
Therefore,
ab = 14 × 47 = 658
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Post by ABC Singh on Oct 26, 2014 21:42:52 GMT 5.5
Thank you
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