题目

1：
Prove that if x is a positive integer that is not divisible by 5,then x4 -1 is divisible
by 5.
（证明如果X是可被5整除的整数,那么X的四次方-1也能被5整除）
2：
Prove that there do not exist two positive integers x and y such that x2-4y2 = 14.
Additional information:you have all known for a long time that there are many
solutions to the equation x2 + y2 = z2,where x,y and z are all positive integers.
This problem considers a slightly dix0berent,but similar looking,type of equations.
Hint:use an indirect proof,and start by factoring x2 - 4y2.
（证明不存在两个数使得x方-4y方=14
提示：用间接证明从因式分解x方-4y方开始））
证明结果有可能是真命题也有可能是假命题.
PS：这不是高等数学证明题,只是非数学课学证明方法的课后题,不会用到大二大三那种很高深的数学..
上面翻译错了.
（证明如果X是不可被5整除的整数,那么X的四次方-1可以被5整除）

提问时间：2020-06-06

答案