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 🙂
Simply superb sir..!! its very useful 🙂
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 🙂
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 – 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 – 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…:)