Saturday, February 5, 2022

2022/015) What are the prime numbers P that make 37P+4 the square of a number?

if is a square let it be $x^2$ 

$37p + 4= x^2$

or $37p = (x^2-4)  = (x-2)(x+2)$

as p is prime so one number is 37 and another is prime or one number is 37p and another number is 1

if x -2 = 1 then x +2 is 5 so it is not 37p

difference between x -2 and x+ 2 is 4 so numbers are 37 and 41 or 37 and 33.

but 33 is not prime so p = 41  

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