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Number Theory Problem 31

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  • Abhishek Kumar

    Jun 20th, 2018

Model Answer:

Consider numbers of the form 6k, 6k+1, 6k+2, 6k+3, 6k+4, 6k+5.

Let us consider numbers greater than or equal to 6.

Such a prime number can only be of the form 6k+1 or 6k+5

as numbers of the rest of the forms are obviously composite.

Hence, the squares of such primes is of the form 6k+1 only.

Therefore, p2+2 is of the form 6k+3, a composite number.

p2+2 is composite for p=5.

Hence, p2+2 is a composite number.

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Author

Abhishek Kumar

Abhishek Kumar

Abhishek did B. Tech. in Computer Science & Engineering from IIT Kanpur in 2005. Thereafter he joined Indian Revenue Service (IRS) in 2006. He has deep interests in science. He authored the book “Mathematics for Learning Physics”, published by Arihant Publications. This book is designed to be used as the first book after class X and addresses difficulty faced by fresh pass-outs from class X in understanding Physics of class XI on account of non-familiarity with mathematical tools(calculus etc)