Question

for all a,b,c are integers, there exists an integer solution to ax^2 +bx^2=c whenever gcd(a,b)|c. Prove this

Answer 1

gcd(a,b)|c
what does this mean?

Answer 2

gcd(a,b) divides c

Answer 3

greatest common divisor

Answer 4

gcd?
means greatest common divisor?

Answer 5

yep

Answer 6

if the equation has integral solutions i.e.
-b+- sqrt(b^2+4ac)
----------------
2a
are integers
hence b^2 + 4ac is a perfct square