This is immensely useful.. thanks for the wonderful article.
I noticed a small error though. In the introduction:

“Equations involving difference and addition of two numbers, say x and y, will give solution over the set of integers only when either both x and y are odd or both are even.”

it be both “Sum and difference of x and y” that should be even or odd rather than x and y both being even or odd for solution over the set of integers.

Hi Jaskiran you are right the answer for 1215 is 6 and 1547 is 3. as it has facotr 1547= 17*13*7 so total 6/2 =3

hiccup
on May 20, 2012 at 8:26 am

@Prashant,
really nice article.
what if only the integral solution is asked and the perfect square is 135^2
suppose the question is (a-35)(b-35)=135^2,then find the number of integral solutions.

yeah we are doing our best to come up with more awesome content..:)

Iconoclast
on April 24, 2012 at 6:34 am

Great… although, I never made a request for maths & quant related stuff but always wanted that. There are many who also feels so but never make a request.

Please continue this initiative. Waiting for more articles on quant & DI.

Simply awesome cleared lot of confusion wat an article sirjeee ðŸ™‚

Simply superb sir..!! its very useful ðŸ™‚

Really very impressive. The Article is very plausible. I am happy to see that how artistically the base concept is used to explain the topic.

looking forward for few more ðŸ™‚

This is immensely useful.. thanks for the wonderful article.

I noticed a small error though. In the introduction:

“Equations involving difference and addition of two numbers, say x and y, will give solution over the set of integers only when either both x and y are odd or both are even.”

it be both “Sum and difference of x and y” that should be even or odd rather than x and y both being even or odd for solution over the set of integers.

correct me if I’m wrong.

great article…too good:)

Amazing write up, best part were the generalizations.. Gonna be super useful.

Respect to you author.. ^_^

Puneet Sir What an article!

In question

5. Find the number of positive integer solutions of equation x2 â€“ y2 = 1215 ?

Answer : 10

1215 can be broken into 5 * 3^5 .. so the number of factors are 6 .. not 10 ??? plz tel me where am I wrong..

same is the case in question.

3. Find the number of positive integer solutions of equation x2 â€“ y2 = 1547 ?

Hi Jaskiran you are right the answer for 1215 is 6 and 1547 is 3. as it has facotr 1547= 17*13*7 so total 6/2 =3

@Prashant,

really nice article.

what if only the integral solution is asked and the perfect square is 135^2

suppose the question is (a-35)(b-35)=135^2,then find the number of integral solutions.

Great work sir…desperately waiting 4 ur more upcoming posts..:)

yeah we are doing our best to come up with more awesome content..:)

Great… although, I never made a request for maths & quant related stuff but always wanted that. There are many who also feels so but never make a request.

Please continue this initiative. Waiting for more articles on quant & DI.

ahh great we could be of such service..:)

Awesome work Puneet Chhabra..

Short cut plus concept clarification..Great.

Thanks a lot .

Will wait for other articles.

thanks a lot amit..

yeah would do our best to keep it rolling…:)