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Home » Mathematics » Advanced Maths » How to find number of solutions of equation involving difference of perfect squares?

How to find number of solutions of equation involving difference of perfect squares?







16 Comments

  1. ron
    ron on November 9, 2014 at 7:58 pm

    Simply awesome cleared lot of confusion wat an article sirjeee 🙂

    Reply
  2. Aravinth
    Aravinth on October 26, 2013 at 10:00 am

    Simply superb sir..!! its very useful 🙂

    Reply
  3. Aadesh Saxena
    Aadesh Saxena on June 4, 2013 at 9:48 am

    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 🙂

    Reply
  4. Venkatesh
    Venkatesh on April 6, 2013 at 6:58 am

    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.

    Reply
  5. vivekanand3435
    vivekanand3435 on January 21, 2013 at 3:47 am

    great article…too good:)

    Reply
  6. Mukund
    Mukund on September 19, 2012 at 11:07 am

    Amazing write up, best part were the generalizations.. Gonna be super useful.
    Respect to you author.. ^_^

    Reply
  7. Amit Mishra
    Amit Mishra on June 4, 2012 at 4:43 pm

    Puneet Sir What an article!

    Reply
  8. jaskiran
    jaskiran on May 27, 2012 at 12:20 pm

    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 ?

    Reply
    • Charanjeet Singh
      Charanjeet Singh on October 13, 2012 at 6:16 am

      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

  9. hiccup
    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.

    Reply
  10. Prateek
    Prateek on April 25, 2012 at 6:07 pm

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

    Reply
    • prashant
      prashant on April 26, 2012 at 8:59 am

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

  11. Iconoclast
    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.

    Reply
    • prashant
      prashant on April 24, 2012 at 7:53 am

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

  12. Amit Chhabra
    Amit Chhabra on April 23, 2012 at 5:57 pm

    Awesome work Puneet Chhabra..

    Short cut plus concept clarification..Great.

    Thanks a lot .
    Will wait for other articles.

    Reply
    • prashant
      prashant on April 24, 2012 at 1:38 am

      thanks a lot amit..
      yeah would do our best to keep it rolling…:)

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