JEE Novice - (17)

Number Theory Level 4

( x 2 − x + n ) ∣ ( x 13 + x + 90 ) \large (x^2-x+n) | (x^{13} + x + 90 )

If n n is an integer, find the value of n n .

Note: ' ∣ | ' means "divides".

This question is a part of JEE Novices .


The answer is 2.

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Nihar Mahajan by Nihar Mahajan , 20, India

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2 solutions

Noel Lo
Jun 4, 2015

Sub in x=0, we have n divides 90. Sub in x=1, we have n divides 92. Since n is an integer, n = 1 or 2. Largest possible value of n = 2.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Reynan Henry
May 27, 2015

Set x =0 and x=1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

This is basically an antisolution.

Short cut hehe

Reynan Henry - 6 years ago

In response to Challenge Master :If the value of n n satisfies for more than one value of x x , then basically it can accepted as a solution.

Ross Walker - 6 years ago

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