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Remainder obtained when the expression is divided by 19 – CAT 2004 Question

[latexpage]
Q.)The remainder, when $({15}^{23}+{23}^{23})$ is divided by 19, is
a)4
b)15
c)0
d)18

[CAT 2004 Question, Remainder Question, Number System, CAT Question]

Solution :

We know that $({ a }^{ n }+{ b }^{ n })=(a+b)({ a }^{ n-1 }+{ a }^{ n-2 }{ b }^{ 1 }+{ a }^{ n-3 }{ b }^{ 2 }+………….+{ b }^{ n-1 })$

So, We can conclude from the above formulae that $({ a }^{ n }+{ b }^{ n })$ is always divisible by (a+b).

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