Question

Show that the square of any positive integer cannot be of the form 5q + 2 or 5q + 3 for any integer q-2.



Please tell me really fast guys.....

Answer 1

Answer:

if (q-2)^2 = 5q + 2

then q^2- 4q +4 = 5q+2

       =>q^2-9q+2=0

solving quadratic equation gives non integer values of q

similarly (q-2)^2 = 5q + 3

gives non integer values of q as solution

so there are no positive integer solutions

Step-by-step explanation: