数论证明作业
T1
证明：任意奇数的平方减一是(8)的倍数
证明 :
设一奇数(x)为(2n+1)
( herefore x^2-1=4n^2+4n)
(ecause 2mid2n)
( herefore 8mid4n^2 且 8mid4n)
( herefore 8mid x^2-1)
T2
证明：当(n)时偶数时，(2mid3^n+1),当(n)时奇数时，(2^2mid3^n+1),无论(n)是偶数还是奇数，对任意正整数(alpha>2)都有(2^alpha
mid 3^n+1).
证明：
(ecause 2mid n)
( herefore 3^n末位为奇数，3^n+1为偶数)
( herefore 2mid 3^n+1.)
T3
设(a,bin mathbb{Z})，且(b eq)