If \(x^{45} + 1\) is divided by \(x^5 + 1\), then the remainder will be: যদি \(x^{45} + 1\) কে \(x^5 + 1\) দ্বারা ভাগ করা হয়, তবে ভাগশেষ কত হবে?

Since we are dividing by \(x^5 + 1\),

\[ x^5 \equiv -1 \]

Now,

\[ x^{45} = (x^5)^9 \]

Substitute \(x^5 = -1\):

\[ (x^5)^9 = (-1)^9 = -1 \]

Therefore,

\[ x^{45} + 1 = -1 + 1 = 0 \]

Remainder = Zero

Correct Answer: A