GATE Electrical Engineering (EE) 2021 Solved Papers

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Question : 4 of 65

Marks: +1, -0

Which one of the following numbers is exactly divisible by

(11^{13}+1) ?

$11^{13}+1$
$11^{26}+1$
$11^{39}-1$
$11^{52}-1$

Solution:

Using Algebraic property,

(11^{52}-1)=(11^{26}+1)(11^{26}-1)=(11^{26}+1)(11^{13}-1)(11^{13}+1)

Since

(11^{52}-1)

has factor of

(11^{13}+1)

, hence

(11^{52}-1)

is completely divisible by

(11^{13}+1)

.

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