[NOIP training] [Law + number theory] Application of Euler's function, noip Euler

[NOIP training] [Law + number theory] Application of Euler's function, noip Euler

Problem 1

[Topic]

Given

Obtain multiple groups of data.

Question

Proof: Except for an even number, the numbers of mutual quality are paired.

By.

Therefore, for the sum of each pair, there are a total of pairs.

Then

 

 

Problem 2

[Topic]

Write on the first circle, write on the second circle, and then write their sum between each two numbers on the basis of each previous circle, it is defined as the number of I in the circle I.

Given, please.

 

Question

Proof: The numbers in the circle are adjacent to each other.

A number can only be composed of two numbers in mutual quality and each construction method is unique.

So.