Let n be a non-negative integer. Then the number of divisors of the form "4n + 1" of the number (10)10 . (11)11 . (13)13 is equal to __________.
Answer (integer)
924
Solution
N = 2<sup>10</sup> $\times$ 5<sup>10</sup> $\times$ 11<sup>11</sup> $\times$ 13<sup>13</sup><br><br>Now, power of 2 must be zero,<br><br>power of 5 can be anything,<br><br>power of 13 can be anything<br><br>But, power of 11 should be even.<br><br>So, required number of divisors is <br><br>1 $\times$ 11 $\times$ 14 $\times$ 6 = 924
About this question
Subject: Mathematics · Chapter: Permutations and Combinations · Topic: Fundamental Counting Principle
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