My teacher gave me this tricky problem

Number Theory Level 3

let x x and y y be 2 two digit numbers. y y is obtained by reversing the digits of x x . Suppose they satisfy the equation x 2 − y 2 = m 2 x^2 - y^2 = m^2 for some positive integer m m , find the value of x + y + m x+y+m .


The answer is 154.

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Abhigyan Adarsh by abhigyan adarsh , 20, India

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2 solutions

Jaiveer Shekhawat
Aug 20, 2015

5 Helpful 0 Interesting 0 Brilliant 0 Confused

You can also add in your good solution that why are we taking 11 only. It is because if we take values bigger than that to get a perfect square then we will get the digits a and b greater than 9 which is not possible. I upvoted your solution!

Kushagra Sahni - 5 years, 9 months ago

I did the same :-)

Akshat Sharda - 5 years, 9 months ago

Your solution is perfect but a bit lengthy when you take out the values of a and b and when you take the sq root of 1089. But otherwise the best one and same as mine . upvoted

abhigyan adarsh - 5 years, 9 months ago
Abhigyan Adarsh
Aug 20, 2015

here is my solution

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice question and a BRILLIANT solution too. BTW had the same approach.

Ankit Kumar Jain - 5 years, 9 months ago

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