Ultimate Quant Marathon Blog For IIM CAT

For All Your Quant Queries

Bonus Question 16.07.09

with 10 comments


Find the number of solutions in distinct positive  integers of x^4+y^4=z^4

A) 0                 B) 1                  C) 2                         D) 3                E) More than 3

Written by Implex

July 16, 2009 at 3:27 pm

Posted in Algebra, CAT 2009, Number Thoery, Online CAT, Problem of the week, Problems

Tagged with , , , , , , ,

«
»

10 Responses

Subscribe to comments with RSS.

  1. choice A) 0 ??

    Sam

    July 17, 2009 at 9:34 am

    Reply

  2. rahul,can u tell the solution of this question

    Prateek

    July 17, 2009 at 9:48 am

    Reply

  3. it’s the fermat’s last theorem.And no one till date has been able to prove this.

    x^n + y^n = z^n for n>2 (does not hold).

    yodha

    July 17, 2009 at 3:13 pm

    Reply

  4. answer : 0

    yodha’ sol sounds correct .

    but in case a person isnot aware of fermat’s last theorem then what ??

    nikhil

    July 18, 2009 at 6:52 am

    Reply

    • the solution is right..
      we do not have a perfect solution for this question.

      but intutively we can solve this

      Rahul

      July 23, 2009 at 6:46 am

      Reply

  5. clearly 0 is a solution

    ANKIT PANGHAL

    August 10, 2009 at 10:04 am

    Reply

  6. i would like to clearify that its the fermat rule that
    x^n + y^n = z^n…n>=3 has no sloution…else we can solve it by jst hit n trial and reach the solution

    ANKIT PANGHAL

    August 13, 2009 at 4:27 am

    Reply

  7. Fermat’s last theorem states that there is no NON trivial solution for the equation written above for n > 2. (0,0,0) is always a solution to such equation for all n>0.

    Kshitiz

    October 11, 2009 at 11:36 am

    Reply

  8. In Fermat’s last theorem n is integer. And it has been proven in 1993 by Andrew Wiles and Richard Taylor.

    Kshitiz

    October 11, 2009 at 11:37 am

    Reply

  9. intuitively, the fourth powers are 1,16,81,256,… etc.. for bigger numbers the gap between these fourth powers is too huge to be compensated by a smaller fourth power. so this equation can only be fulfilled among the smaller fourth powers. however as is evident from these numbers, no such combination is possible. so 0

    Pranshu

    November 10, 2009 at 2:46 pm

    Reply

Leave a comment