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The remainder , when (1523 + 2323) is divided by 19, is
Answer & Solution
Correct 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
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
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