## Problem Of The Week 30

**Let b be an odd square and n be any natural number. Then b=n^3+2n^2. Find b?**

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**Let b be an odd square and n be any natural number. Then b=n^3+2n^2. Find b?**

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Written by Implex

September 27, 2008 at 10:31 am

Posted in Number Thoery, Problem of the week

Tagged with Number Theory, Problem of the week

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If we have to find only 1 value

441=7^3+ 2(7)^2 satisfies the condition.

tyroSeptember 27, 2008 at 12:13 pm

Find the smallest b ..

The question is incomplete. sorry!

outtimedSeptember 27, 2008 at 12:48 pm

The smallest value of b will then be 3 as the question does not say perfect square.

3= (1)^3 + 2 (1)^2

tyroSeptember 27, 2008 at 1:41 pm

what does odd square mean, if it is not perfect square????

outtimedSeptember 27, 2008 at 1:48 pm

b= n^3 +2 n^2

= n^2(n+2)

such that b makes for a perfect square. both n^2 and n+2 have to be odd.

so n can be an odd natural number such that b is a perfect square.

so the smallest b is 441 only.

But I still think it should be mentioned as perfect square.

tyroSeptember 27, 2008 at 2:14 pm

yaar odd square means perfect square,

there is nothing called an imperfect square!

outtimedSeptember 27, 2008 at 2:55 pm