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by yellowho » Sat Feb 26, 2011 9:10 pm
When X is divided by Y what is the remainder if x=(y+2)^2? (y is integer greater than 4)

I got 4. Correct? I guess the y>4 is a give away.

x=y^2+4y+4 => x=y(y+4) +4

y= integer, is that a significant fact to determine remainder?
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by Night reader » Sat Feb 26, 2011 9:32 pm
solution didn't suit :( just plug in integer>4 to check remainder is 4
yellowho wrote:When X is divided by Y what is the remainder if x=(y+2)^2? (y is integer greater than 4)

I got 4. Correct? I guess the y>4 is a give away.

x=y^2+4y+4 => x=y(y+4) +4

y= integer, is that a significant fact to determine remainder?
Last edited by Night reader on Sat Feb 26, 2011 10:10 pm, edited 1 time in total.
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by Anurag@Gurome » Sat Feb 26, 2011 9:47 pm
yellowho wrote:...is that a significant fact to determine remainder?
Yes, you're correct.
We can write x = y(y + 4) + 4

Now in general, when x = 2, is divided by y the remainder will be same as the remainder when 4 is divided by y. Thus, if y = 2 or 4, the remainder will be 0; if y = 3, the remainder will be 1; and if y is any integer greater than 4, then the remainder will be 4.
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by HSPA » Tue Mar 01, 2011 12:28 am
x/y = (y+2)^2 / y
= (y+2)+(4/y)

We know y is greater than 4 so (4/y) will have remainder as 4
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