An algebra problem by Razing Thunder

Algebra Level 4

  • Find the sum of all possible values of m and n (m , n are natural numbers) such that 2 m + 3 n 2^{m} + 3^{n} is a perfect square

  • INDIAN mathematical Olympiad question


The answer is 6.

Razing Thunder by Razing Thunder , 16, India

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1 solution

Mahdi Raza
Jul 10, 2020

Short answer: Only possible value is 5 2 = 4 2 + 3 2 ⏟ By Pythagorean theorem = 2 4 + 3 2 ⟹ 6 \underbrace{5^2 = 4^2 + 3^2}_{\text{By Pythagorean theorem}} = 2^{\red{4}} + 3^{\red{2}} \implies \boxed{\red{6}}

To know why this is the only posible value, here's a solution video: here

0 Helpful 0 Interesting 1 Brilliant 0 Confused

I don't know modular arithmetic any else method @Mahdi Raza .

A Former Brilliant Member - 11 months ago

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