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Why did everyone leave? :(

HINT: Linear Diophantine equation.

these problems would be unsolveable and fool will greet us April Fool's Day mmhmm that would be epic

(1) is very much solvable by almost anybody.

both of \( (x, y) \) are not positive??? either x is negative or y is negative or both are negative?

looks like n is greatest common divisor

Diophantine sounds like organic chemistry. I'm googling it.
10?

Lol, he (Diophantus) is the sometimes called the father of algebra.

It took me time but the Linear Diophantine thing is really nice. Thanks.

is the answer of 2 1??

1 is the not the right answer.

......

must be infinity then

No it's not infinity.

There are 11 non negative integral solutions to the given diophantine equation

Am I right?

Well done @2bornot2b!

Thanks!

If other want, you may like to the post the solution too.

And yes for n-10=0, the value is true too.

For 2nd 81*64?

81*64 - 1? lol

haha, nopes :)

0?

i was thinking the same .. lol

but it seems 0 is nowhere close to 81*64

Yeah lol

I'm talking about the second problem.

It is, but at first I presumed it was both x and y can't be non-positive integral :/

If you'll read the first question you might understand the cause of my presumption :/

in that case .. Mr. Math must be right.

The answer of (2) is \(0\), unless something's wrong with the question.

FoolForMath for the 3rd question, Can you tell the value of r(3,2)?

@FoolForMath what do you say??

FoolForMath WHAT SAY YOU?
*This is more cinematic hehe*

What does "is tiled with" mean? (My English is failing me)!

Hmm made up of, maybe

Oh I see.

But why is \(r(2,1)=3\)?

Ishaan, \( r(3,2)=18 \).

no you are trying to find n
is r(3,2)=16?

number of rectangles?? you mean there are lot's of rectangle???

not both postive
ok i see r(3,2)=18

?? lost me on that one

x=inf, y=-1, n = inf

since gcd(81,64)=1 we can solve
\[81x+64y=1\] for x and y and so can solve
\[81x+64y=n\] for any n

x=inf, y=-1, n = inf what about this ??

i have an answer i like for the second to last one

whew. left the house, had a beer and thought about it a little more clearly

Congratz sat! :) You may like to post your solution for others.

not unless everyone is done

Alright:) Third one is the hardest in my opinion. So well done agian! :)

merci

uhm for number 2, do you mean the greatest possible value of n for x<0 and y<0?

Is the answer to the rectangle one 5148?

@satellite73 Am I right?

that is what i got, yes

It's been a while, so
http://ideone.com/k7o4g
My thought process was explained in the comments.

For the complimentary problem, \(a^2\)?

hmm

answer for (2) is it n=-1?

or it could be zero

#2 answer : 5039
Complimentary problem: \( a \)

Oh yeah, a

explanation???