KVPY SA Exam 2013 Question Paper

Question : 13 of 80

Marks: +1, -0

How many natural numbers n are there such that

n!+10

is a perfect square?

Solution:

If n = 1, 2, 4, 5, n! + 10 is not a perfect square
If n = 3, n! + 10 is a perfact square
If n > 5
n! + 10

= {10}↙{\even}[3×4×6×....×(n+1)]↙{\is\odd}

than exponant of 2 is one so it is not a perfact square.

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