The remainder , when (1523 + 2323) is divided by 19, is

Answer: Option C

NOTE: aⁿ + bⁿ is always divisible by (a + b) when n is odd.

So, (15²³ + 23²³) always divisible by 38.
And 38 is a multiple of 19, So, the number which is divisible by 38, is divisible by 19 too.
(15²³ + 23²³) is divisible by 19.
So, $$\frac{{15}^{23}+{23}^{23}}{19}$$   == Remainder ⇒ $$\frac{15+23}{19}$$  == Remainder ⇒ $$\frac{38}{19}$$ == Remainder ⇒ 0