The Stair-Step Approach in Mathematics by Hayk Sedrakyan & Nairi Sedrakyan

Author:Hayk Sedrakyan & Nairi Sedrakyan
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

where .

Solution.

We have that

Note that the equation

does not have a positive integer solution. We proceed the proof by contradiction argument. Assume that

Thus, it follows that

Hence, we obtain that either or . This leads to a contradiction.

Therefore, the smallest odd number satisfying the assumptions of the problem is equal to 9.

Problem 4. Find the smallest number that is possible to represent at least in twenty different ways as , where m, n are non-negative integers.

Solution.

Assume that a is the required number, then , where , , , . Let . We have that

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