Problem of 2017

Algebra Level 2

$\large a^2-b^2=2017$

For $a,b\epsilon \mathbb N$ that equation is true.

Then find the value of $ab=?$

This is a Zebra's Algebra series problem.

1018081 1016064 4068289 It's not possible for

a,b\epsilon \mathbb N

1017072 2017

2 solutions

Md Mehedi Hasan
Nov 9, 2017

$\large {a^2-b^2=2017\\\Rightarrow (a+b)(a-b)=2017}$

$2017$ is a prime number. If we factorize it, we get $2017=2017\times1$

So we can write, $a+b=2017\\a-b=1$

Solving that we get, $a=1009, b=1008$

And so the answer is: $ab=1009\times1008=1017072$

Peter van der Linden
Nov 12, 2017

The difference between the nth and nth+1 square equals 2n+1. So if the difference is 2017 then n = 1008 = b. So a = 1009.