KVPY 2019 SA Exam Previous Papers

Question : 13 of 80

Marks: +1, -0

Let

N_1 = 2^55 + 1

and

N_2 = 165.

Then

Solution:

165 = 3 × 5 × 11

∵x + y divides

x^n + y^n

∴ 32 + 1 divides

32^11 + 1^11

Hence N

_1

is multiple of 33, simultaneously unit digit in N

_1

is 9 so it not the multiple of 5
Hence HCF of N

_1

& N

_2

is 33

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