Binomial Theorem
Remainder using Binomial Expansion
Grade 11
Question:
<p>If <i>13<sup>99</sup></i> is divided by 81, the remainder is 46. The value of <i>a</i> is</p>
<p>(a) 13</p>
<p>(b) 23</p>
<p>(c) 39</p>
<p>(d) 55</p>
Step-by-Step Solution
Key Concept: Express the base as a sum relative to the divisor and use binomial expansion to isolate the remainder.
<p><strong>Solution:</strong></p><p>Use binomial expansion: <i>13<sup>99</sup> = (12+1)<sup>99</sup></i>.</p><p>Expand using binomial theorem and find remainder when divided by 81.</p>
Correct Answer: c