• 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