What a problem 4!

Number Theory Level 3

True or False?

Let p , q , k , x , y p,q,k,x,y be positive integers, then if p p and q q can be expressed as 20 k + 3 20k+3 or 20 k + 7 20k+7 , then there is a solution for p q = x 2 + 5 y 2 pq= x^2+5y^2 .

True False

Mohammad Farhat by Mohammad Farhat , 16, Singapore

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1 solution

Aryan Gupta
Oct 27, 2018

since its not mentioned that x and y must be intergers then for any 5y^2 there must be an x to equate pq

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