Why does the Diophantine equation 6x−8y=156x - 8y = 156x−8y=15 have no integer solutions?
Because gcd(6,8)=2\gcd(6, 8) = 2gcd(6,8)=2, which does not divide 151515.
Because the left side is always even for any integers xxx and yyy, while the right side is odd.
Because 6x−8y6x - 8y6x−8y is always negative.
Because there are no prime factors of 151515 that are also factors of 666 or 888.