Question

The remainder, when $19^{200}+23^{200}$ is divided by $49$ , is_______

Answer 1

The correct answer is 29.
(21+2)200+(21−2)200
⇒2[100C0​21200+200C2​21198⋅22+…..+200C198​2122198+2200]
⇒2[49I1​+2200]=49I1​+2201
Now ,2201=(8)67=(1+7)67=49I2​+67C0​67C1​⋅7=
49I2​+470=49I2​+49×9+29
∴ Remainder is 29