密码学 数论入门 Euler Theorem 实战

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• 利用欧拉定理找一个0~9之间的数a，使得7^1000模10与a同余（注意这等于7^1000的十进制展开的最后一位）

Euler' sTheorem:

for every (a,n) that are relatively prime to Ø(n) is a conginent model.

a ^Ø(n) =1 mod n

This condition, a is between 0 to 9 that is conginent model to 7^1000 mod 10

such that 7 Ø(0~9) =1 mod 10

=7^1000 mod 10

=7^5 * 7^200 mod 10

=(7^5 mod 10)^200

=1

Therefore , a=1

• 利用欧拉定理，找一个位0~28之间的整数x，使得x^85 模35与6同余