# Please find the minimum value:

a,b are natural no's .
2013+$$a^2$$=$$b^2$$.
Find the minimum possible value of ab?

Note by Kandarp Singh
3 years, 9 months ago

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658?

- 3 years, 9 months ago

yeah but how

- 3 years, 8 months ago

hi. See that $$a^2-b^2=(a+b)(a-b)=2013$$. And since $$a$$ and $$b$$ are integers, so have to be $$a+b$$ and $$a-b$$. Then you can work out the factors of $$2013$$ to get $$a$$ and $$b$$, and then it's easy to tell which one will give the minimum product.

- 3 years, 9 months ago

In general I simply find max{|a-b|} for ab to be minimum

- 3 years, 9 months ago