Introduction to Math Olympiad Problems by Michael A. Radin

Author:Michael A. Radin [Radin, Michael A.]
Language: eng
Format: epub, pdf
ISBN: 9780367544829
Publisher: CRC Press
Published: 2021-04-14T00:00:00+00:00

Similar to the technique in Example 3.3, for we set

First notice that for all , 3n and are both even integers. Second of all observe that is a multiple of 3. We can then prove that must be a multiple of 8 (this will be left as an end of chapter exercise). Hence the result follows.

The following example will analyze the ending digit of specific neighboring perfect squares.

Example 4.10. Let n be a positive integer (). Determine the ending digit of if the ending digit of is 9 and the ending digit of is 4.

Solution:

As the ending digit of n2 is 9, then n must be an odd perfect square and therefore n must be an odd integer. Thus we can first conclude that must be an even integer and must be an odd integer.

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