## Dhaka Secondary 2011/2 (Junior 2011/4)

**Forum rules**

Please

**don't post problems (by starting a topic)**in the "Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.

### Dhaka Secondary 2011/2 (Junior 2011/4)

$A$ is the product of seven odd prime numbers. $A \times B$ is a perfect even square. What is the minimum number of prime factors of $B$?

### Re: Dhaka Secondary 2011/2

are the seven odd prime numbers distinct?

**A man is not finished when he's defeated, he's finished when he quits.**

### Re: Dhaka Secondary 2011/2

yes, they are distinct

"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor

### Re: Dhaka Secondary 2011/2

then the ans is 8.

Let, $A=p_1.p_2...p_7$ none of them are same or 2. So $B=2.2.p_1.p_2...p_7$ then the ans is 8

Let, $A=p_1.p_2...p_7$ none of them are same or 2. So $B=2.2.p_1.p_2...p_7$ then the ans is 8

**A man is not finished when he's defeated, he's finished when he quits.**

### Re: Dhaka Secondary 2011/2 (Junior 2011/4)

bro i did not get your solution, can u describe it even more clearly??@hasib bro

### Re: Dhaka Secondary 2011/2 (Junior 2011/4)

shifat, i am giving an example. suppose $A= 3\times 5\times 7\times 11\times 13\times 17\times 19$ and as $A\times B$ is an even perfect square, it should look like this $A\times B= 2^2\times 3^2\times 5^2\times 7^2\times 11^2\times 13^2\times 17^2\times 19^2\times $(any other perfect square) . thus we get $B=2^2\times 3\times 5\times 7\times 11\times 13\times 17\times 19\times $(any other perfect square). so the minimum prime factors of $B$ are $2$, $3$, $5$, $7$, $11$, $13$, $17$, $19$. so the answer is $8$. Hasib has just used $p_{1}$, $ p_{2}$, $ p_{3} $..... in lieu of $3$, $5$, $7$.... that's it

অম্লান সাহা

### Re: Dhaka Secondary 2011/2 (Junior 2011/4)

oh, got it, thanks.....

### Re: Dhaka Secondary 2011/2 (Junior 2011/4)

What's a perfect even square?

- Phlembac Adib Hasan
**Posts:**1016**Joined:**Tue Nov 22, 2011 7:49 pm**Location:**127.0.0.1-
**Contact:**

### Re: Dhaka Secondary 2011/2 (Junior 2011/4)

Perfect even squares = The squares of even numbers.

Welcome to BdMO Online Forum. Check out Forum Guides & Rules