定理若p为正整数,k为半偶数,则(p~2+k)(1/2)是无理数.先给出半偶数的概念:能被2整除但不能被4整除的偶数称为半偶数.如2,6,10,14等.注意,定理中的半偶数的条件是必要的,否则定理不真.如(2~2+12)(1/2)=16不是无理数,原因为12不是半偶数.下面用穷举反证法分两部分证明定理. Theorem If p is a positive integer and k is a semi-even number, then (p ~ 2 + k) (1/2) is an irrational number. The concept of semi-even numbers is given first: an even number divisible by 2 but not divisible by 4 is called a half Even numbers, such as 2, 6, 10, 14, etc. Note that the semi-even conditions in the theorem are necessary, otherwise the theorem is not true, such as (2 + 2 + 12) 12 not semi-even numbers. The following is an exhaustive proof in two parts to prove the theorem.