# Understand the problem

Find all positive integers such that equation has a solution in integers and .

# Start with hints

##### Source of the problem

Belarus MO 2018 Problem 10.5

##### Topic

Number Theory

##### Difficulty Level

5/10

##### Suggested Book

An Introduction to Number Theory

Do you really need a hint? Try it first!

Let’s check for n = 1. Observe that a = 27, b = 13 gives a solutions for n = 1. What about higher degrees? Can we use this information?

Does it work for n = 2? Let’s prove something general! Prove that for a, b to have solutions, n must be odd.

If n is even, Take to see that , which has no integer solutions in . Hence, n must be odd.

Well now take n odd. Say for some positive integer . Then, the solution exists and works.

# Watch video

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How can i cheak the answers..

Which answers? They are provided in the last hint always. All the best. Hope you are loving the Sequential Hints Method!