Find the number of pairs of positive integers.

rahul · 11-12-2009, 11:43 AM

Find the number of pairs of positive integers (x, y) such that x^6 = y^2 + 127.

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

pavitran · 23-01-2010, 02:32 PM

As my knowledge ......

x^6 -y^2 =127

Lets assume z=x^3

z^2 - y^2 =127
(z+y)(z-y) =127

127 is a prime number so possible combination is 1, 127.
x and y are positive,
z+y =127 ----- (1) and z-y =1 ----- (2)
solving (1) and (2) we get x=4, y=63

Which Competitive Exams Question Papers you find this Question!

If there is any other procedure for these type of questions.

11-12-2009, 11:43 AM	#1
rahul Member Join Date: Dec 2009 Posts: 58 Rep Power: 15	Find the number of pairs of positive integers. Find the number of pairs of positive integers (x, y) such that x^6 = y^2 + 127. (A) 0 (B) 1 (C) 2 (D) 3 (E) 4

23-01-2010, 02:32 PM	#2
pavitran Member Join Date: Jan 2010 Location: Mandavalli,Chennai,India Posts: 12 Rep Power: 0	As my knowledge ...... x^6 -y^2 =127 Lets assume z=x^3 z^2 - y^2 =127 (z+y)(z-y) =127 127 is a prime number so possible combination is 1, 127. x and y are positive, z+y =127 ----- (1) and z-y =1 ----- (2) solving (1) and (2) we get x=4, y=63 Which Competitive Exams Question Papers you find this Question! If there is any other procedure for these type of questions.