Question

find no. of triplets of prime number (p,q,r),satisfying 3p^4-5q^4-4r^2=26​

Answer 1

Given :   3p⁴  - 5q⁴  - 4r²  = 26

To find : number of triplets of prime numbers (p, q, r) satisfying

Solution:

3p⁴  - 5q⁴  - 4r²  = 26

By Doing hit & Trial Method

p = 5

q = 3

r = 19

3p⁴  = 3(5)⁴  =   1875

5q⁴  = 5(3)⁴  = 405

4r² = 4(19)² = 1444

1875 - 405 - 1444

= 1875 - 1849

= 26

( 5 , 3 , 19) is the  triplets of prime numbers (p, q, r) satisfying  3p⁴  - 5q⁴  - 4r²  = 26

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