IIT JEE , AIEEE Forum - Mathematics , Algebra

man111

Q2 THe number of positive integral solutions of x to the power 4 + y to the power 4 = 3789108

rahulr

no positive integral solution exists.... :)
infact....no integral solution exists ....

hsbhatt

From Fermat's "Little" Theorem, a^p-1 is divisible by p if p is a prime and a is prime to p

Hence, for p = 5, a⁴ - 1 is divisible by 5. a⁴is of the form 5k+1

Hence x⁴ + y⁴ leaves a remainder 2 when divided by 5 when x and y are not multiples of 5. 3789108 on the other hand leaves a remainder 3. You can similarly eliminate cases when x or y or both are multiples of 5.

Hence, there are no integral solutions.

rahulr

above method is correct...but i doubt if it is in the IIT JEE syllabus or not....
i m saying coz i used old methods to solve the problem....which are a bit lengthy but definitely within the course...

soham406

Fermats theorem is regarded as the fundamental property of numbers so there no question of it being in the portion or not

rv_hbk

ANS is 0.

This is because 4th power of any even no.(ending in2,4,6,8) ends in6.

4th power of any odd no. except 5 ends in 1.

4th power of 5 ends in 5.

So there's no way that sum of 4th power of 2 nos. ends in 8.

ANS=0 SOLUTION.

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